1 ACT Section (1) 1 . In the figure below, measure of BAC is 35, the measure of ABC is 115, what is the measure ACD? A Geometry 4. In ABC shown below, ̅̅̅̅ ̅̅̅̅ and the measure of A is 48. What is the measure of C? C 35 48 A 115 C B B A. 48 B. 84 C. 90 D. 96 E. 132 D A. 115 B. 120 C. 125 D. 145 E. 150 2. In the figure below, the measure of XAB is 150, the measure of YCB is 81, and X, A, C, and Y are collinear. What is the measure of B ? 5. In the figure below, QPR is 40, PQR is 105, And points Q, R, and S are collinear. What is the measure of PRS ? P F. 105 G. 125 H. 130 J. 140 K. 145 F. 30 G. 51 H. 60• J. 69• K. 77• 105 ? S R Q 6. In the figure below, ̅̅̅̅ is congruent to ̅̅̅̅ , and ̅̅̅̅ and ̅̅̅̅ intersect ̅̅̅̅ at C. what is the measure of B? B 3. In the figure below, what is the value of x? ? x x C E 38 A 107 A. 35 B. 38 C. 72 D. 107 E. 145 Mr . Mosaad El Geneady 35 A. 14 B. 38 C. 76 D. 104 E. 142 Mo: 01001851053 F 2 ACT 7. In the figure below, C is on ̅̅̅̅ , BAC is 42, and ABC is 108, What is the measure of ACD ? A Geometry 10. In the figure below, BAC measures 35, ABC is 95, and points B, C, and D are collinear What is the measure of ACD ? A 42 ? 108 B C D A. 108 B. 120 C. 132 D. 138 E. 150 35 F. 95 G. 125 H. 130 J. 140 K. 145 95 B ? C D 11. The figure is shows lines ⃡ and ⃡ , line segments ̅̅̅̅ and ̅̅̅̅ , and 2 angle measures. What is the measure of ACB ? 8. Three line segments intersect as shown in the figure below, forming angles with measure of 150, 40, and x, respectively . What is the value of x? F. 38 G. 42 H. 48 J. 55 K. 77 F. G. H. J. K. 12. In the figure below, C lies on both ̅̅̅̅ and ̅̅̅̅ , ̅̅̅̅ and ̅̅̅̅ are parallel and congruent, and 2 angle measures are given. What is the measure ofACB ? 95 85 80 75 70 9. In the figure below, ⃡ intersects ⃡ at C and is perpendicular to ⃡ . Line ⃡ intersects ⃡ at F. Given that the measure of EFG is 25, what is the measure of BCD? F. 65 G. 115 H. 120 J. 130 K. 155 Mr . Mosaad El Geneady F. 55 G. 57.5 H. 65 J. 67.5 K. 70 13. In The above figure, l //m. What is the value of x? A) 40 B) 25 C) 20 Mo: 01001851053 D) 15 E) 10 ACT 14. In the figure below, Vertices D and F of DEF lie on ̅̅̅̅ , the measure of CDE is 148, and the measure of EFG is 140. What is the measure of DEF ? F. 72 G. 98 H. 100 J. 108 K. 116 15. Given the triangle shown below with exterior angles that measure x°, y°, and z° as shown, what is the sum of x, y, and z ? F. 180 G. 231 H. 309 J. 360 K. Cannot be determined from the given information 16. In the figure below, C is the intersection of ̅̅̅̅ and ̅̅̅̅ . If it can be determined, what is the measure of ∠BAC ? A. 080° B. 100° C. 110° D. 115° E. Cannot be determined from the given information Mr . Mosaad El Geneady 3 Geometry 17. In the figure below, BAC measures 30°, ABC measures 110°, and points B, C, and D are collinear. What is the measure of ACD ? F. 150° G. 140° H. 130° J. 120° K. 110° 18. In the figure below, A,D,C, and E are collinear. ̅̅̅̅, ̅̅̅̅, and ̅̅̅̅ are all the same length, and the angle measure of ABD is 25. What is the measure of BCE ? F. 50 G. 100 H. 105 J. 130 K. 160 19. In the figure below, lines m and n are parallel, transversals r and s intersect from an angle of measure x, and 2 other angle measures are as marked. What is the value of x? A. 15 B. 25 C. 35 D. 65 E. 80 Mo: 01001851053 ACT 20. The figure below shows quadrilateral ABCD , What is the measure of C? F. 120 G. 115 H. 105• J. 100• K. 80• 21. In the figure below, B is on ̅̅̅̅ , E is on ̅̅̅̅ , ̅̅̅̅ is parallel to ̅̅̅̅ and ̅̅̅̅ is congruent to ̅̅̅̅ . What is the measure of DEB ? F. 35 G. 135 H. 145• J. 155• K. 215• 22. In the figure below, ̅̅̅̅ is perpendicular to ̅̅̅̅ , the measure of CED is 38, what is the measure of AEB ? F. 38 G. 45 H. 52• J. 71• K. 76• Mr . Mosaad El Geneady 4 Geometry 23. In the figure below, measure of ABE is 75, the measure of ABC is 25, and the measure of DBE is 35. What is the measure ABD A. 15 B. 30 C. 40 D. 50 E. 60 24. In the figure below, ABCD is a trapezoid, E lies on ⃡ , and angle measures are as marked, What is the measure of BDC? F. 15 G. 25 H. 30 J. 35 K. 45 25. In the figure below, ̅̅̅̅̅ intersect ̅̅̅̅ at Y, the measure of XYV is ( 3x + 5), and the measure of ZYW is ( 4x – 6). What is the measure of XYZ ? F. 83 G . 97 H. 104 J. 142 K. 160 Mo: 01001851053 5 ACT 26. In ABC below, the measure of ABC is 70, the measure ACB is 32, D is on ̅̅̅̅ , and ̅̅̅̅ is a bisector of BAC. What is the measure of ADB Geometry 29. The parallelogram below has consecutive angles with measure xand 25. What is the value of x? C 32 A. 100 B. 115 C. 130 D. 140 E. 155 D A. 64 B. 70 C. 71 D. 78 E. 102 70 A x 25 B 27. In the figure below, line m is perpendicular to line n, and line p is parallel to line q, Lines m. n, and p intersecting at a single point. Some angle measures are given. What is the value of x? 30. In the figure below, 5 angles measure are given. The angle marked with measure of yis an exterior angle. What is the value of y? ( x + 25 ) ( 2x + 10 ) ( 3x – 25 ) F. 32 G. 58 H. 122 J. 148 K. 158 Mr . Mosaad El Geneady y F. 22.5 G. 45 H. 80 J. 100 K. 145 31. In the figure below ,B lie on ̅̅̅̅ , E lie on ̅̅̅̅ , ̅̅̅̅ // ̅̅̅̅ , DBF is isosceles with ̅̅̅̅ ̅̅̅̅ , and CBF is 32. What is the measure of BED? 28. In the figure below, E is on ̅̅̅̅ , and the measure of BED and AEB are 90 and 145, respectively. If it can be determined, what is the measure of CED? A. 35 B. 45 C. 55 D. 80 E. Cannot be determined from the given information ( 2x – 10 ) F. 106 G. 116 H. 122 J. 132 K. 148 Mo: 01001851053 6 ACT 32. In the figure below, A is on ⃡ and C is on ⃡ What is the measure of ABC ? . A. 24 B. 42 C. 45 D. 48 E. 66 33. In ACD below, B is on ̅̅̅̅ , the measure of CAD is 28, and ̅̅̅̅ is perpendicular to both ̅̅̅̅ And ̅̅̅̅. What is the measure of CBE? Geometry 35. For trapezoid ABCD shown below, AB//DC, the measures of the interior angles are distinct, and the measure of D is x. What is the degree measure of A in terms of x ? F. (180 – x) G. (180 – 0.5 x) H. (180 + 0.5 x) J. (180 + x) K. is x 36. In ABC, the sum of the measures of ∠A and ∠B is 47°. What is the measure of ∠C ? A. 47° B. 86° C. 94° D. 133° E. 143° 37. In a plane, the distinct lines ⃡ and ⃡ intersect at A, where A is between C and D. The measure of BAC is 47°. What is the measure of BAD ? F. 104 G. 118 H. 124 J. 146 K. 152 A. 043° B. 047° C. 094° D. 133° E. 137° 34. In the figure is below, ̅̅̅̅ and ̅̅̅̅ intersect at D. What is the measure EAD? 38. In the figure below, ̅̅̅̅ //̅̅̅̅ , ̅̅̅̅ bisects BAC, And ̅̅̅̅ bisects ACD. If the measure of BAC is 82°, what is the measure of AEC ? F. 30 G. 47 H. 50• J. 53• K. 70• Mr . Mosaad El Geneady A. 86° B. 88° C. 90° D. 92° E. Cannot be determined from the given information Mo: 01001851053 ACT 7 Geometry 1. In the figure below, ̅̅̅̅ is congruent to ̅̅̅̅ , and ̅̅̅̅ and ̅̅̅̅ intersect ̅̅̅̅ at C. what is the measure of B? 4. In the figure below, Lines ⃡ and ⃡ are cut by Transversals ⃡ and ⃡ that intersect at E. Two angle measure are given, What is the measure of ABD ? A. 28 B. 31 C. 62 D. 118 E. 149 F. 110 G. 112 H. 138 J. 144 K. 146 2. In Isosceles PQR shown below, ̅̅̅̅ ̅̅̅̅ and the measure of P is 54. If it can be determined, What is the measure of Q ? 5. In the figure is below, line l and line m are parallel. line a and line b are intersect line l at the same point. What is the value of x? Section (2) F. 36 G. 54 H. 72• J. 81• K. Cannot be determined from the given information 3. In the figure below, ̅̅̅̅// ̅̅̅̅ , A measure 41, C measure 110and ADB measure 122. What is the measure of CBD ? A. 17 B. 41 C. 53 D. 63 E. 6 Mr . Mosaad El Geneady A. 6 B. 11 C. 14 D. 18 E. 30 6. In the figure is below, ⃡ is parallel to ⃡ , B lies on ⃡ and ⃡ , F lies on ⃡ , the measure of ABC is 132, and EBG GBF FBD. What is the measure of BFD? A. 84 B. 86 C. 88 D. 89 E. 92 Mo: 01001851053 8 ACT Geometry Use the following information to answer questions 10 - 12. In the parallelogram ABCD shown below, the diagonals intersect at E, mBDC = 42, mBDA = 71, and AB = ( ) inches x l 35 m 60 k s t 7. In the figure below, line l is parallel to line m and line k is parallel to line s. What is the value of x? 10. What is mBAD? A. 65° B. 80° C. 85° D. 95° E. 115° A. 23 B. 42 C. 48 11. Given that DC = ( value of n? 8. In the figure s below, parallel lines a and b intersect parallel lines c and d. If it can be determined, what is the sum of measure of 1 and 2? F. 2 G. 4 E. 71 ) inches, what is the H. 6 J. 12 K. 36 12. Suppose A and B are located at (2,10) and (30,3), What is the coordinates of E A. ( B. ( F. 220 G. 180 H. 140• J. 110• K. Cannot be determined from the given information D. 67 ) ) C. ( D. ( E. ( ) ) ) 13. In parallelogram ABCD, ̅̅̅̅ is a diagonal . the measure of ABC is 40, and the measure of ACD is 57. What is the measure of CAD ? 9. In triangle ABC in the figure above, x = 89. What is the value of y? A) 8 B) 10 C) 13 D) 16 Mr . Mosaad El Geneady E) 19 A. 40 B. 57 C. 77 D. 83 E. 97 Mo: 01001851053 ACT 14. In the figure below, ̅̅̅̅ and ̅̅̅̅ intersect at C, and ̅̅̅̅ //̅̅̅̅ . Which of the following angles must have the same measure as BAC ? F. ACB G. ACD H. BCE J. CDE K. CED 15. Lines a, b, c, and d are shown below and a // b. Which of the following is the set of all angles that must be supplementary to ∠x ? 9 Geometry 18. In the figure below, line l is parallel to line m. Transversals t and u intersect at point A on l and intersect m at points C and B, respectively. Point X is on m, the measure of ∠ ACX is 130°, and the measure of ∠ BAC is 80°. How many of the angles formed by rays of l, m, t,and u have measure 50° ? A. 4 B. 6 C. 8 D. 10 E. 12 19. For the triangles in the figure below, which of the following ratios of side lengths is equivalent to the ratio of the perimeter of ABC to the perimeter of DAB ? F. {1, 2} G. {1, 2, 5, 6} H. {1, 2, 9, 10} J. {1, 2, 5, 6, 9, 10} K. {1, 2, 5, 6, 9, 10, 13, 14} 16. In the figure below, B lies on ̅̅̅̅ , ̅̅̅̅ bisects ABE, and ̅̅̅̅ bisects CBD. What is the measure of DBE ? A. 90° B. 60° C. 45° D. 30° E. Cannot be determined from the given information 17. In isosceles trapezoid ABCD, ̅̅̅̅ is parallel to ̅̅̅̅ DC, BDC measures 25°, and BCA measures 35°. What is the measure of DBC ? F. AB:AD G. AB:BD H. AD:BD J. BC:AD K. BC:BD 20. In right triangle ACD shown below, B lies on Side ̅̅̅̅ . Some angle measures are given. What is the measure of BDC ? A. 25° B. 35° C. 50° D. 55° E. 60° A. 85° B. 95° C. 105° D. 115° E. 125° Mr . Mosaad El Geneady Mo: 01001851053 10 ACT 21. In the figure below, ̅̅̅̅, ̅̅̅̅ , and ̅̅̅̅ all intersect at point Z. the measure of 2 angles are given. What is the measure of CZE ? Geometry 24. In the figure below, lines l and m are parallel, Line n is a transversal, and 3 angle measure are Given. What is the value of x – y ? x l y 50 A. 76 B. 102 C. 104 D. 119 E. 129 F. G. H. J. K. 22. In the figure below. line is parallel to line m. What is the measure of BOD? B A 35 D m A. 35 B. 75 C. 85° D. 105° E. 145° 23. In the figure above, what is the value of x ? A. B. C. D. E. B A 140 C 25. Triangle ABC, the measure of A is 43, the measure of BAC is (4y), and the measure of BCD is (11y). What is the measure of B? l O 18 20 16 14 22 Mr . Mosaad El Geneady m –80 50 80 130 180 43 A. 12° B. 48° C. 89° D. 91° E. 132° (4y) (11y) C D 26. In parallelogram ABCD below, the measure of BCD is 38, What is the measure of BDA? A. B. C. D. E. 38° 41° 44° 49° 52° Mo: 01001851053 11 ACT 27. In the figure below, ̅̅̅̅ = ̅ , the measure of ABC is 80, the measure of ADC is 100, What is the measure of BAC? Geometry 30. In the figure below, A is on ⃡ and C is on ⃡ What is the measure of ABC ? . A. 24 B. 42 C. 45 D. 48 E. 66 A. B. C. D. E. 80° 100° 120° 60° 70° 31. In the figure is below, ̅̅̅̅ and ̅̅̅̅ intersect at D. What is the measure EAD? 28. In right triangle ACD shown below, B lies on Side ̅̅̅̅ . Some angle measures are given. What is the measure of BDC ? A. 25° B. 35° C. 50° D. 55° E. 60° F. 30 G. 47 H. 50 J. 53 K. 70 29. In the figure below, ̅̅̅̅ is congruent to ̅̅̅̅ , and ̅̅̅̅ and ̅̅̅̅ intersect ̅̅̅̅ at C. what is the measure of B? 32. In any parallelogram ABCD, it is always true that the measures of ∠ABC and ∠BCD: A. 28 B. 31 C. 62 D. 118 E. 149 F. add up to 180°. G. add up to 90°. H. are each greater than 90°. J. are each 90°. K. are each less than 90°. Ans:F 33. In ABCD , A measure greater than 43 and A measure exactly 90. Which of the following phrases best describes the measure of C ? A. Greater than 47 B. Equal to 47 C. Equal to 60 D. Equal to 133 E. Less than 7 Mr . Mosaad El Geneady Mo: 01001851053 ACT 34. What is the measure of the smaller angles formed by the line and the ray shown in the figure below A. 14 B. 28 C. 29 D. 58 E. Cannot be determined from the given information 35. Marie is building a kite. In a drawing of her kite, shown below, AB = BC, AD = DC, The measure of ABC is 48, and the measure of ADC is 50, What is the of BAD ? A. 50 B. 65 C. 90 D. 115 E. 130 36. In the figure below, ̅̅̅̅ is perpendicular to ̅̅̅̅ , is perpendicular to ̅̅̅̅ , and ̅̅̅̅ ̅̅̅̅ . Which of the following congruences is NOT necessarily true? F. ̅̅̅̅ ̅̅̅̅ G. ̅̅̅̅ ̅̅̅̅ H. ̅̅̅̅ ̅̅̅̅ J. DAB CBA K. AB EBA Mr . Mosaad El Geneady 12 Geometry 37. In the figure below, A, D, B, and G are collinear. If CAD measures 76°, BCD measures 47°, and CBG measures 140°, what is the degree measure of ACD ? F. 12° G. 14° H. 17° J. 36° K. 43° 38. In the figure below, A, B,C, and E are collinear. and ̅̅̅̅, ̅̅̅̅ , and ̅̅̅̅ are all the same length, and angle ABD is as marked. What is the measure of BCE? F. 50 G. 100 H. 105 J. 130 K. 160 39. A rectangle has an area of 32 square feet and a perimeter of 24 feet. What is the shortest of the side lengths, in feet, of the rectangle? F. 1 G. 2 H. 3 J. 4 K. 8 40. If ∠A and ∠B are acute angles, then ∠A and ∠B CANNOT be (A) vertical angles (B) complementary angles (C) supplementary angles (D) congruent angles (E) adjacent angles Mo: 01001851053 ACT 13 Geometry 41. The measure of QOR is 140, the measure of 3 angles are given in term of x. What is the measure of QOS ? F. 96 G. 100 H. 120• J. 138• K. 140 • 42. In ABC below, D,E, and F are points on ̅̅̅̅ , ̅̅̅̅ and ̅̅̅̅ . ̅̅̅̅ ̅̅̅̅ . What is the sum of measures of the angles marked x and y? F. 40 G. 80 H. 90• J. 100• K. 130 • 45. In Figure 9, points A, B, C, and D are all on the circle with center O. If BDA measures 25°, and ∠CAD measures 32°, what is the measure of BOC in degrees? A. 33 B. 66 C. 123 D. 147 E. 303 46. In ABC below, points A, C, E, and G are collinear; and D, E, and F are collinear. What is the measure of EFG? A. 40 B. 45 C. 60 D. 80 E. Cannot be determined from the given information 47. What is the measure of each exterior angle of a regular pentagon? 44. In Figure 4, WX WZ and XY ZY . n A. 50 B. 142 C. 25 D. 26 E. 168 Mr . Mosaad El Geneady (A) 90 (B) 60 (C) 120 (D) 108 (E) 72 48. How many lines of symmetry does a rhombus have? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 Mo: 01001851053 ACT Section (3) 1. Shown below are similar triangles ABC and DEF with A D and B E. The given Lengths are in inches. What is the length of ̅̅̅̅ ? A. 3 B. 4 C. 4 D. 5 14 Geometry 4. In the figure below, ABC and DEF are similar triangles. What is the perimeter of DEF? A. 3 B. 8 C. 11 D. 12 E. 13 5. In the figure below, E is on ̅̅̅̅ and C is on ̅̅̅̅. What is the length of ̅̅̅̅? E. 6 2. Shown below are right triangles ACD and ABE with lengths given in inches. What is the length of ̅̅̅̅ ? A. 5 B. 5 F. 2,640 G. 2,784 H. 3,960 J. 4.400 K. 5,840 C. 5 D. 6 E. 8 3. In right triangle ADE shown below, ̅̅̅̅ // ̅̅̅̅ What is the length of ̅̅̅̅ ? 6. In right triangle ACE below, is parallel to , and is perpendicular to at D. The length of is 20 feet, the length of is 3 feet, and the length of is 4 feet. What is the length, in feet, of ? A. B. C. D. 3 E. 5 Mr . Mosaad El Geneady A. 10 B. 12 C. 15 D. 16 E. 17 Mo: 01001851053 15 ACT 7. Surveyors want to determine a pond`s length, represented by ̅̅̅̅ in the figure below. They place stakes at points A, B, C,D, and E so that C is the intersection of ̅̅̅̅ and ̅̅̅̅ and so that ̅̅̅̅ is parallel to ̅̅̅̅ . The distances between certain stakes are shown in the figure. What is the pond`s length, in meter? F. G. H. J. K. 46 52 56 62 67 8. In the figure shown below, ̅̅̅̅ // ̅̅̅̅ , BD = AD, D and E are on ̅̅̅̅ and ̅̅̅̅ , respectively, AC = 8ft And the height of ABC is 10 ft. What is DE, in ft? F. G. H. J. K. Geometry 9. Lines l1 and l2 intersect each other and 3 parallel Lines, l3, l4, and l5,at the points shown in the figure below. The ratio of the perimeter of ABC to the perimeter of AFG is 1:3. The ratio DE to FG is 2:3. What is the ratio AC to CE? F. 1:1 G. 1:2 H. 1:3 J. 2:1 K. 3:1 10. The triangles below are similar ( ABC DEF) Which of the following is an expression for the area of ABC? 2 3 4 5 6 F. ( )( ) G. ( )( ) H. ( )( )( ) 9. In the figure above, ABC is similar to DEF What is the value of y? A. 3 B. 4 C. 4.5 D. 5 E. 6 Mr . Mosaad El Geneady J. ( ) ( ) K. ( )( ) Mo: 01001851053 ACT 11. Marisa`s design for a rectangle stained glass window with 7 triangles is shown below. The 2 white triangles are congruent ( ABC DEC) What is the measure of CED? A. 45° B. 65° C. 70° D. 115° E. 135° 12. In the figure above, ABC and DEF are similar. What is the length of DF? A. 3 B. C. D. 7 E. 13. In the figure shown below, ABC DEF, sides ̅̅̅̅ and ̅̅̅̅ are 7.2 cm long, side ̅̅̅̅ is 10.8 cm the measure of E is 42. What is the measure of C ? A. 42 B. 46 C. 60 D. 63 E. 69 Mr . Mosaad El Geneady 16 Geometry 14. Given the 2 similar right triangles shown below with dimension given in inches, What is the area of the smaller triangle? A. 1 B. 3 C. 4 D. 6 E. 12 15. In the figure shown below, E and G lie on ̅̅̅̅ , D and F lie on ̅̅̅̅ , ̅̅̅̅ and ̅̅̅̅ are parallel to ̅̅̅̅ , What is the length of ̅̅̅̅ ? A. 9 B. 18 C. 21 D. 30 E. 36 16. In the figure shown below, ABC DEF, sides ̅̅̅̅ and ̅̅̅̅ are each 7.2 cm long, side ⃡ is 10.8cm long, and the measure of E is 42. What is the measure C ? A. 42 B. 46 C. 60 D. 63 E. 69 Mo: 01001851053 17 ACT Geometry 17. In the figure below, ̅̅̅̅ is parallel to ̅̅̅̅, E is the midpoint of ̅̅̅̅. F is the midpoint of ̅̅̅̅ . G is the midpoint of ̅̅̅̅ , and H is the midpoint of ̅̅̅̅ . The lengths marked are in inches. What is the length of ⃡ , in inches? 20. In the figure above, ABE is similar to ACD. What is the value of x? F. 31 G. 31 H. 37 J. 38 K. 43 (A) 3 (B) 3.5 (C) 3.75 (D) 4 (E) 13.75 18. In the figure is shown below, ̅̅̅̅ // ̅̅̅̅ , ̅̅̅̅ and ̅̅̅̅ intersect at B. what is the length of ̅̅̅̅ ? 21. In right triangle ABC, ̅̅̅̅ ̅̅̅̅ . If AB = 6, AC = 8, BC = 10, and DE = 4, find EC. A. B. C. 5 D. 6 E. F. G. H. J. K. 6 8 9 10 11 19. The ratio of the side lengths for a triangle is exactly 12:14:15. In a second triangle similar to the first, the shortest side is 8 inches long. To nearest tenth of an inch, what is the length of the longest side of the second triangle 22. Two triangles are similar. The shortest side of the smaller triangle is 9 inches long, and the shortest side of the larger triangle is 16 inches long. The perimeter of the smaller triangle is 36 inches. What is the perimeter of the larger triangle? F. 43 G. 48 H. 57 J. 61 K. 64 A. 11.0 B. 10.0 C. 9.3 D. 6.4 E. Cannot be determined from the given information Mr . Mosaad El Geneady Mo: 01001851053 ACT 23. Points B and C lie on ̅̅̅̅as shown below. The length of ̅̅̅̅ is 30 units; ̅̅̅̅ is 16 units long; and ̅̅̅̅ is 220 units long, How many unit long if it can be determine, is ̅̅̅̅ ? F. 4 G. 6 H. 10 J. 14• K. Cannot be determined from the given information 24. As shown below, A, B, C, and D are collinear, with B between A and C, and with C between B and D. Given AC = BD = 12cm and given BC = 3cm, what is the length of AD? 18 Geometry 26. What is the maximum number of distinct diagonals that can be drawn in the hexagon shown below? A. 4 B. 5 C. 6 D. 9 E. 12 27. Shown below is a regular hexagon inscribed in a circle whose radius is 4 inches. What is the perimeter of the hexagon? A. 8 B. 12√ C. 18 D. 20 E. 24 F. 9 G. 15 H. 18 J. 21 K. 27 28. Shown below is a regular hexagon inscribed in a circle whose radius is 4 inches. What is the perimeter of the hexagon? 25. In pentagon ABCDE, shown below, A measures 50.What is the total measure of the other 4 interior angles? F. 30 G. 30√ H. 60 J. 60√ K. 60√ 29. What is the measure of each exterior angle of a regular pentagon? F. 130 G. 200 H. 310• J. 432• K. 490• Mr . Mosaad El Geneady A. 90 B. 60 C. 120 D. 108 E. 72 Mo: 01001851053 ACT 30. In the figure below, the measure of 4 angles of pentagon ABCDE are given, What is the measure of A? A. 100 B. 108 C. 120 D. 140 E. 160 31. The measure of interior angles of a pentagon are 70, 100, 110 and 135, respectively. What is The measure of the 5th interior angle? F. 35 G. 55 H. 83 J. 108 K. 125 32. The degree measures of the interior angles of a certain pentagon are in ratio 2:3:4:4:5. What is the measure of the last interior angle of this pentagon? A. 30 B. 60 C. 90 D. 120 E. 150 19 Geometry 34. How many sides does a regular polygon have if Each interior angle measures 140? A. 6 B. 7 C. 8 D. 9 E. 10 35. Five points are shown on each of the 2lines in the figure below. Point O is the intersection point of the 2 lines. Which of the following rays does NOT contain point O? F. G. H. J. K. 36. In the regular heptagon shown below, what is The sum of the measures of the 7 interior angles? F. 360 G. 720 H. 900 J. 1,080 K. 1,260 33. All six sides of the polygon shown below are congruent. What is the value of x? 37. The midpoints of the sides of rectangle WXYZ are vertices of rhombus ABCD . The dimensions of rectangle WXYZ are 6cm by 8cm. What is the perimeter of rhombus ABCD ? A. 258 B. 240 C. 220 D. 180 E. 165 F. G. H. J. K. Mr . Mosaad El Geneady 20 25 28 40 36 Mo: 01001851053 20 ACT Section (4) 1. A parallelogram ABCD shown below. What is the area of the parallelogram Geometry 4. In the figure shown below, ̅̅̅̅ ̅̅̅̅, and rectangle ABCD has a length of 6 inches and a width of 4 inches. The area of rectangle EFGD is 2 times the area of rectangle ABCD. What is the length of ̅̅̅̅ F G 4 A. 18 B. 36 C. 39 D. 45 E. 72 2. What is the perimeter, in feet, of the figure shown below? 8 ft 20 ft C 6 F. G. H. J. K. D A E 2 2.4 3.5 4 4.8 5. A square is circumscribed about a circle of 7 cm radius. What is the area of square? 14 ft 20 ft A. B. C. D. E. 60 62 70 80 8 3. The figure shown below, all angles are right angles, and the sides lengths are in yards. What is the area of the figure? F. 49 G. 56 H. 98 J. 49 K.196 B C 9 4 150 10 A 6 D 4 F. 12 G. 74 H. 98 J. 110 K. 134 11 Mr . Mosaad El Geneady 6. The area of parallelogram ABCD above is A. 12 B. 20 C. √ D. √ E. 24 Mo: 01001851053 21 ACT Geometry 7. What is the area of the parallelogram shown below 6 in 13 8 5 in 20 10 in A. 42 B. 50 C. 55 D. 60 E. 75 8 10. A corner is cut from a rectangular sheer of paper to produce the pentagon shown in the figure above. What is the perimeter of the pentagon ? 8. The figure shown below, all angles are right angles, and the sides lengths are in yards. What is the area of the figure? A. 49 B. 52 C. 61 D. 62 E. 76 6 11. In the figure below is composed of a square BCDE and equilateral triangle ABE. The length of ̅̅̅̅ is 6 inches. What is the perimeter of ABCDE ? 9 3 13 F. 42 G. 75 H. 93 J. 99 K. 117 9. If the area of KLMN in the figure below is 12cm2, What is the length of ̅̅̅̅ ? K 5 cm 12. The figure shown below, all angles are right angles, and the sides lengths are in yards. What is the area of the figure? 45 F. G. H. J. K. 2√ 5√ 6√ 2√ √ Mr . Mosaad El Geneady 18 24 30 42 45 L ? N A. B. C. D. E. M F. 49 G. 71 H. 86 J. 105 K. 120 Mo: 01001851053 22 ACT 13. The interior of a rectangular shipping crate has dimensions 2ft by 3ft by 6ft. The crate will be filled with cube-shaped boxes whose exteriors have dimensions 12in by 12in by 12in. Given that no box can extend beyond the dimensions of the crate1s interior, what is the maximum number of boxes the cart can hold? A. 3 B. 12 C. 36 D. 48 E. 72 14. A rectangular solid has a volume of 100 cubic units, If the length, width, and height of the solid are each doubled, what will be the volume of the new solid be? Geometry 17. The length of hypotenuse of a certain right triangle is 50 inches, and the length of one of its leg is 40 inches. What is the length of the other leg of the triangle F. G. H. J. K. 10 30 45 64 90 18. The floor plan oh Helena`s kitchen is shown in the figure below; the given dimensions are in feet, Helena will install baseboard along the bottom of each wall ( shown by solid lines in the floor plan). According to the floor plan, which of the following distances is closest to the perimeter of Helena`s kitchen? 10 F. 200 G. 400 H. 600 J. 800 K. 2,700 15. The ratio of the radii of 2 circles is 4:9. What is the ratio of their circumferences? F. 2 : 3 G. 4 : 9 H. 16 : 81 J. 4 : 8 K. 9 : 18 16. All of the following statements concern triangles that are similar, congruent, or both. Which statement is FALSE? A. Triangles that are congruent are always similar B. Lengths of corresponding sides of similar triangles are always equal. C. Lengths of corresponding sides of congruent triangles are always equal. D. Measure of corresponding angles of similar triangles are always equal. E. Measure of corresponding angles of congruent triangles are always equal Mr . Mosaad El Geneady 8 19 F. 40 G. 50 H. 60 J. 100 K. 120 19. In the figure below, the area of the larger square is 50 square centimeters and the area of the smaller square is 18 square centimeters. What is x, in centimeters? F. 2 G. 2√ H. 4√ J. 16 K. 32 Mo: 01001851053 23 ACT 20. In the 8-sided figure below, adjacent sides meet at right angles and the lengths given are in meters. What is the perimeter of the figure, in meters? Geometry 23. In the figure is below, E lies on ̅̅̅̅ . The area of AED is what fraction of area of rectangle ABCD ? 8 12 20 A. A. 40 B. 80 C. 120 D. 160 E. 400 B. C. D. E. 21. Roger will pour concrete to make a sidewalk with the dimensions in feet, shown in the figure below. He will pour the concrete to a depth of 4 inches. One bag of concrete mix makes 0.6 cubic feet of concrete. What is the least whole number of bags of concrete mix that Roger needs in order to make the sidewalk? F. G. H. J. K. 20. What is the area of the figure below ? F. G. H. J. K. 16 44 50 58 67 60 80 275 375 450 21. In the figure below, what is the perimeter of the Figure below? 3 22. In the figure is shown below, all angles are right Angles, and the lengths given in meters. What is The area of the figure? 2 7 1 8 4 F. G. H. J. K. 12 52 68 80 96 10 Mr . Mosaad El Geneady 4 A. 10 B. 12 C. 13 D. 14 E. 16 Mo: 01001851053 ACT 22. The base length of isosceles trapezoid ABCD shown below, and E is on ̅̅̅̅ . What is the ratio of area of ABCD to the area of AED? A. 2 : 1 B. 4 : 1 C. 5 : 1 D. 10 : 1 E. 20 : 1 23. In quadrilateral ABCD shown below, ̅̅̅̅ // ̅̅̅̅, BC = 20 inches, AD = 28 inches, and the distance between ̅̅̅̅ and ̅̅̅̅ is 7 inches. What is the area of quadrilateral ABCD? A. 140 B. 168 C. 196 D. 336 E. 560 24 Geometry 25. A rectangle that is c inches by d inches is in the interior of a rectangle that is a inches by b inches. As shown below. The area of the shaded region is What fraction of the area of the large rectangle, In term of a, b, c, and d ? A. B. C. D. E. ( )( ) 26. Squares with sides of length x cm have been removed from each corner of a rectangle measuring 8 cm by 18 cm, resulting in the figure below. In term of x, what is the area of the figure 24. Square ABCD shown below, has a side length of 10 inches. Point D is the midpoint of ̅̅̅̅ and F is the midpoint of ̅̅̅̅ . What is the ratio of the area of DEF, shown shaded , to the area of pentagon ABCDF? F. 52 – 4x2 G. 144 – 4x2 H. 144 + 4x2 J. 144 – 8x K. 144 – 52x + 4x2 A. 1: 3 B. 1: 4 C. 1: 7 D. 1: 8 E. 1: 10 Mr . Mosaad El Geneady 27. One side of square ABCD has a length of 18 meters. A certain rectangle whose area is equal to the area of ABCD has a width of 6 meters. What is the length of the certain rectangle? A. B. C. D. E. 18 24 27 30 54 Mo: 01001851053 25 ACT 28. A square has a perimeter of 20 feet. What is the Area of the square? F. 5 G. 10 H. 25 J. 40 K. 80 29. The sides lengths of a certain triangle are 4, 6, 7 Which of the following descriptions best classified this triangle ? F. Scalene acute G. Scalene right H. Scalene obtuse J. Isosceles obtuse K. Isosceles right Geometry 32. The perimeter of 1 of the 25 congruent squares is how many meters? F. G. H. J. K. 1 4 5 20 25 34. The lengths of corresponding sides of 2 similar right triangles are in ratio 2:9. The hypotenuse of the smaller triangle is 8 inches long. How many inches long is the hypotenuse of the larger triangle ? F. G. H. J. K. 4.5 11 15 18 36 30. In the figure below shows 12 congruent line segments, each determined by a pair of adjacent points. The sum of the lengths of the 12 line segments is 36 cm. Each intersection of 4 of the line segments forms 4 right angles. What is the area of the shaded region? 35. For ABC shown below, base ̅̅̅̅ has a length of 16 inches and altitude ̅̅̅̅ has a length of 8 inches The area of a certain square is equal to the area of ABC. What is the length of side of the square? A. 4 B. 6 C. 9 D. 12 E. 16 F. 6 G. 8 H. 12 J. 16 K. 32 31. The dimension of equilateral triangle ABC are given in the figure below. What is the value of y? 36. The lengths of 2 legs of right triangle ABC shown below . The midpoint of ̅̅̅̅ is how many inches from A? F. G. H. J. K. A. 16 B. 20 C. 21 D. 28 E. 40 2 5 8 13 16 Mr . Mosaad El Geneady Mo: 01001851053 26 ACT Geometry Section (5) 1. In square ABCE shown below, D is the midpoint of ̅̅̅̅ . Which of the following is the ratio of the area of ADE to the area of ADB ? Use the following information to answer questions 5-9 . In the figure is shown below, ABCD is a rectangle, EFGH is a square, and ̅̅̅̅ is a diameter of a semicircle . Point K is the midpoint of ̅̅̅̅ . Point J is the midpoint of both ̅̅̅̅ and ̅̅̅̅ . Points E and F lie on ̅̅̅̅ . F. 1:1 G. 1:2 H. 1:3 J. 1:4 K. 1:8 2. In DEF, the length of ̅̅̅̅ is √ cm, and the length of ̅̅̅̅ is 3 cm, What is length of ̅̅̅̅ ? F. G. H. J. K. 3 √ √ √ Cannot be determined from the given information 3. Laura plane to paint the 8-foot-high rectangular walls of her room, and before she buys paint she needs to know the area of the wall surface to be painted. Two walls are 10 feet wide, and the other 2 walls are 15 feet wide. The combined area of the 1 window and the 1 door in her room is 60 square feet. What is the area of the wall surface Laura plane to paint ? A. 200 B. 340 C. 360 D. 390 E. 400 5. The length of ̅̅̅̅ is what percent of the length of ̅̅̅̅? A. 15.6% B. 30% C. 36% D. 43.2% E. 50% 6. What is the length of ̅̅̅ ? F. 13 G. 15.6 H. 17 J. √ K. √ 7. What is the length of arc ̂ ? A. 2.5 B. 5 C. 6.25 D. 10 E. 25 4. The edges of a cube are each 3 inches long. What is the surface area, in square inches, of this cube? F. 9 G. 18 H. 27 J. 36 K. 54 Mr . Mosaad El Geneady 8. The figure will be placed in the standard (x,y) coordinate plane so that K is at origin, ̅̅̅̅ is parallel to the x-axis, and 1 meter equal 1 coordinate unit. Which of the following values could be the y-coordinate of H? F. 1.8 G. 3.6 H. 8.4 J. 10 K. 12 Mo: 01001851053 27 ACT 9. In the figure below, the border of a pool and the border of a patio surrounding that pool are similar rectangles. What is the length of the pool ? Geometry 13. The empty container shown below is a right rectangular prism with dimensions given in inches. How many cubic inches of liquid are needed to fill the container to 75% of its capacity F. G. H. J. K. A. 30 B. 40 C. 42 D. 48 E. 52 10. In the figure below, 2 nonadjacent sides of a regular pentagon (5 congruent sides and 5 congruent interior angles) are extended until they meet at point X. What is the measure of ∠ X A. 18° B. 30° C. 36° D. 45 E. 72 148 240 444 720 960 14. The length of a rectangle is 4 inches longer than the width. The perimeter of the rectangle is 28 inches. What is the width of the rectangle? A. 5 B. 7 C. 10 D. 12 E. 14 15. A right prism with triangular bases and with dimensions given in inches is shown below. What is the prism`s total surface area ? 11. The perimeter of parallelogram is 80 inches, and The length of 1 side is 18 inches, If it can be determined, what are the lengths of other 3 sides? F. G. H. J. K. 18, 13, 13 18, 18, 26 18, 22, 22 18, 31, 31 Cannot be determined, from the given information 12. Distinct line l and m intersect, forming 4 pairs of adjacent angles. Which of the following statements must be true about these 4 pairs of angles? F. The difference of the angle measures in each pair is less than 45 G. The difference of the angle measures in each pair 90 H. The measures of each angle in each pair is 45 J. The sum of angle measures in each pair is 90 K. The sum of angle measures in each pair is 180 Mr . Mosaad El Geneady F. G. H. J. K. 120 204 228 240 264 16. How long, in centimeters, is 1 side of a square Whose perimeter is equal to the circumference Of a circle with radius od 2 centimeters? A. B. C. 4 D. 16 E. 4 Mo: 01001851053 28 ACT 17. The line below contain X,Y and Z, in that order. The ratio of the length of ̅̅̅̅ to the length of ̅̅̅̅ Is 5:9. If it can be determined, what is the ratio of the length of ̅̅̅̅ to the length of ̅̅̅̅? Geometry 20. A-foot-wide brick sidewalk is laid around a rectangular swimming pool. The outside edge of the sidewalk measures 30 feet by 40 feet, as shown in the figure below. What is the perimeter, in feet, of the swimming pool? A. 5: 14 B. 5: 4 C. 9: 5 D. 14: 5 E. Cannot be determined from the given information 18. In ABC below, D is the midpoint of ̅̅̅̅, BAC is a right angle, AB = 8m and AC = 10m. What is AD, in meters? F. √ G. √ H. √ J. √ K. √ 19. In the diagram below, B, F, and H are on ̅̅̅̅ , ̅̅̅̅ , and ̅̅̅̅ , respectively, and ̅̅̅̅ ̅̅̅̅. The area of square ABGF is the area of square ACDE. What percent of the area of ACDE does the shaded Portion represent? A. 0.0625% B. 0.125% C. 0.25% D. 6.25% E. 12.5% Mr . Mosaad El Geneady A. 70 B. 116 C. 140 D. 816 E. 1,200 21. A circle has a circumference √ feet. What is the area, in square feet, of the circle? A. B. C. D. E. √ √ 22. The height and radius of the right circular cylinder below are given in meters. What is the volume of the cylinder ? A. 30π B. 31π C. 150 π D. 180π E. 900π Mo: 01001851053 29 ACT Geometry 23. What is the volume of a right circular cone with radius 3 inches and height 6 inches? ( Note : the volume of right circular cone with radius r and height h is ) 26. The volume of a sphere is , where r is the radius of the sphere. What is the volume of a sphere with diameter 4 yards? A. 6 B. 12 C. 18 D. 27 E. 36 F. G. H. 32 J. 48 K. 24. A cube with edges 4 cm long is inscribed in a sphere, as shown below. What is the radius of the sphere in centimeter? F. G. H. J. K. 2√ 2√ 4√ 4√ 2 25. The figure below shows a solid concrete ramp for skateboarding. The length is 10 feet, the width is 6 feet, and the height is 3 feet. Which of the following values id closest to the volume in cubic feet, of the concrete used to construct thr ramp? 27. A father and his son are standing near to each other on level ground late one afternoon so that their shadows end at the same place. The father is 75 inches tall, the son is 50 inches tall, and the The father`s shadow is 120 inches long, as shown in figure below. Which of the following is closest to the distance, d inches, between the father and his son? F. G. H. J. K. 25 40 60 70 80 28. To nearest 1 foot, what is the height of rectangular prism with base length of 15 feet, and base width 1 feet, and a volume of 100 cubic feet? F. G. H. J. K. 5 7 9 20 75 29. The area of a rectangle is 300 square meters, and its length is 3 times its width. How many meters wide is the rectangle? F. 32 G. 76 H. 90 J. 115 K. 180 Mr . Mosaad El Geneady F. 10 G. 30 H. 50 J. 100 K. 150 Mo: 01001851053 30 ACT 30. The angle measure of CDE are shown below, Point B lie on ̅̅̅̅, and point C lie on ̅̅̅̅ . What is the value of cos( + )? Geometry 34. Kamini is constracting the kite shown below. The kite include 2 perpendicular supports, one of length 40 inches and the other of length 28 inches The ends of the supports are connected with string to form 4-sided figure that is symmetric with respect to the longer support. A layer of paper will cover the interior of the 4-sided figure. Which of the following is closest to the area that Kamini will cover with paper? F. 0 G. H. √ √ J. K. 1 A. 101 B. 280 C. 560 D. 840 E. 980 31. A formula of the volume ,V, of a right circular cylinder is V = r2h, where r is the radius and h is the height. The cylindrical tank shown below has radius 6 meters and height 5 meters and is filled with water. 35. An 8 inch by – 6-inch rectangle is cut along a diagonal to form 2 triangles. What is the area of each triangle? Given that the weight of 1 cubic meter of water is approximately 2,205 pound, the weight, in pounds, of the water in the tank is: 36. Two sides of a triangle are equal of length. The third side is 3 cm longer than either of the other 2 sides. Given that the perimeter of the triangle is 93 cm, what is the length of the longest side? F. less than 400,000. G. between 400,000 and 900,000. H. between 900,000 and 1,200,000. J. between 1,200,000 and 1,700,000. K. more than 1,700,000. 32. Two concentric circles have radii of 5 centimeters and 6 centimeters, respectively. How many centimeters longer is the circumference of the larger circle than that of the smaller circle A. 1 B. C. 2 D. 11 E. 22 Mr . Mosaad El Geneady F. 7 G. 12 H. 14 J. 24 K. 48 Ans:J A. B. C. D. E. 29 30 31 33 34 37. What is the area of a right triangle with side Lengths 10cm, 26cm, and 24cm? A. 432 B. 312 C. 260 D. 240 E. 120 Mo: 01001851053 31 ACT Geometry Section (6) 1. The rectangle shown in the figure shown below is partitioned into 3 triangles, 2 of which are shaded What is the total area of the 2 shaded regions 5. In the figure below, QRS is equilateral, side ̅̅̅̅ is bisected by T, and side ̅̅̅̅ is bisected by U. What is the degree measure of TUS? F. G. H. J. K. F. 60 G. 90 H. 120 J. 135 K. 150 20 24 32 40 80 2. A parallelogram has a perimeter of 84 inches, and 1 of its sides is 16 inches, If it can be determined, What are the lengths of other 3 sides? F. G. H. J. K. 16, 16, 36 16, 18, 18 16, 26, 26 16, 34, 34 Cannot be determined from the given information 3. A rectangular box that is foot deep, 2 foot wide, and 1 foot long has a volume of how many cubic feet? F. G. 1 H. 2 J. 9 K. 81 4. A 3-inch-tall rectangular box with a square base is constructed to hold a circular pie that has a diameter of 8 inches. Both are shown below. What is the volume of the smallest such that it can hold this pie? A. 24 B. 64 C. 72 D. 192 E. 512 Mr . Mosaad El Geneady 6. A 5-inch-by-7-inch photograph was cut to fit exactly into 4-inch-by-6-inch frame. What is the area of part of the photograph that was cut off ? A. 2 B. 10 C. 11 D. 12 E. 24 7. The length of a rectangle is 12 feet. The width of the rectangle is the length. What is the perimeter of the rectangle ? F. G. H. J. K. 18 24 30 36 72 17. The total surface area, T, of any right circular cone with a radius r and a slant height s, such as the cone shown below, can be determined by using the formula T = r2 + rs. If a cone has a 3-inch radius and a 5-inch slant height, what is total surface area? F. 18 G. 24 H. 40 J. 75 K. 135 Mo: 01001851053 ACT Use the following information to answer questions 18-20 The top view and side view of a 40-foot-long swimming pool are shown in the figure below. all dimensions given are in feet. 32 Geometry 20. A full lap is 2 times the length of the pool. Johann swam 5 full laps of the pool in 4 minutes. Which of the following values is closest to Johann`s average swimming speed, in feet per minute? F. 35 G. 45 H. 60 J. 90 K. 120 The top view shows the top rectangular surface of the Pool and the surrounding rectangular patio. All 4 walls of the pool are vertical and perpendicular to the top surface. The side view shows a cross section along the length of the pool. All cross sections parallel to the side view are congruent. The shallow end has a constant depth of 4 ft. The deep end has a constant depth of 9ft. A rectangular surface connects the shallow and deep ends. 18. What is the area of the patio surrounding the pool? F. 500 G. 600 H. 900 J. 1,100 K. 1,350 19. Johann put up a fence along the outer edge of the patio. Given that the material for the fence cost $12 per foot, what was the total cost of the material for the fence? A. $1,020 B. $1,320 C. $1,800 D. $3,040 E. $3,360 Mr . Mosaad El Geneady 21. The side view of the pool is placed in the standard (x,y) coordinate plane, keeping the same orientation and scale, such that both vertical segments showing depth are parallel to the y-axis. Which of the following values is closest to the slope of the line segment connecting the shallow end to the deep end? A. –0.44 B. –0.63 C. –0.75 D. –1.33 E. –1.60 22. The volume of a right circular cone with radius r and height h is , Cones A and B are both right circular cones. The radius of Cone B is 2 times the radius of cone A. Cone B`s height is Cones A`s height. Compared to the volume of Cone A, the volume of Cone B is: A. The same. B. as greater. C. as greater. D. 2 times as greater E. 4 times as greater 23. The perimeter of rectangle ABCD is 96 cm. The ratio of the side lengths AB : BC is 3:5. What is the length of ̅̅̅̅ ? A. 6 B. 18 C. 30 D. 36 E. 60 Mo: 01001851053 ACT 24. From point A outside a circle and in the same plane as the circle, 2 rays are drawn tangent to the circle with the points of tangency labeled B and C, respectively. Segment ̅̅̅̅ is then drawn to form ABC. If A measures 70, what is the measure of ABC? F. 70 G. 55 H. 40 J. 35 K. Cannot be determined from the given information 25. A line contain points A, B, C, and D. Point B is between points A and C. Point D is between points C and B. which of the following inequalities must be true about the lengths of these segments? F. BC < AB G. BD < AB H. BD < CD J. CD < AB K. CD < BC Ans: 26. The perimeter of rectangle ABCE is 96cm. the ratio of the side lengths AB:BC is 3:5. What is length of ̅̅̅̅? A. 6 B. 18 C. 30 D. 36 E. 60 27. Toby wants to find the volume of a solid toy soldier. He fills a rectangular container 8cm long, 6cm wide, and 10 cm high with water to a depth of 4 cm. Toby totally submerges the toy soldier in the water. The height of the water with the submerged toy soldier is 6.6 cm. Which of the following is closest to the volume of the toy soldier? A. 125 B. 156 C. 192 D. 208 E. 317 Mr . Mosaad El Geneady 33 Geometry 28. The length of a rectangle is 5 inches longer than the width . The perimeter of the rectangle is 40 inches. What is the width of the rectangle? F. G. H. J. K. 7.5 8 15 16 17.5 29. Each side of square ABCD has a length of 50cm. A certain rectangle whose area is equal to the area of ABCD has a width of 10cm. What is the length of the rectangle A. 40 B. 50 C. 60 D. 125 E. 250 30. In DEF, the length of ̅̅̅̅ is √ cm, and the length of ̅̅̅̅ is 6 cm, What is length of ̅̅̅̅ ? F. G. H. J. K. 6 √ √ √ Cannot be determined from the given information 31. The length of a rectangle is 5 inches longer than the width. The perimeter of the rectangle is 40 inches. What is the width of the rectangle ? F. 07.5 G. 08 H. 15 J. 16 K. 17.5 32. A room has a rectangular floor that is 15 feet by 21 feet. What is the area of the floor in square yards? A. 24 B. 35 C. 36 D. 105 E. 144 Mo: 01001851053 ACT 34. The lengths of the legs of a right triangle are 4 miles and 5 miles. Which of the following is closest to that of the hypotenuse of the right triangle F. 3.0 G. 4.5 H. 6.4 J. 12 K. 36 A 35. The parallel sides of the isosceles trapezoid shown below are 10 feet long and 16 feet long, What is the distance, between these 2 sides? A. 3 B. 4 C. 5 D. 10 E. 16 34 Geometry 38. A rectangle has area of 32 square feet and a perimeter of 24 feet. What is shortest of the lengths of the rectangle ? F. 1 G. 2 H. 3 J. 4 K. 8 39. In the figure below, points E and F are the midpoints of sides and ̅̅̅̅ of rectangle ABCD, point G is the intersection of AF and , and point H is the intersection of and . The interior of ABCD except for the interior of EGFH is shaded. What is the ratio of the area of EGFH to the area of the shaded region? 36. What is the perimeter, in inches, of the isosceles right triangle shown below, whose hypotenuse is 8√ inches long? A. 8 B. 8 + 8√ C. 8 + 16√ D. 16 E. 16 + 8√ 37. The length of a rectangle is 3 times the length of a smaller rectangle. The 2 rectangles have the same width. The area of the smaller rectangle is a square units. The area of the larger rectangle is kA square units. Which of the following is the value of k ? F. 1:2 G. 1:3 H. 1:4 J. 1:6 K. Cannot be determined from the given information 40. In the figure below, ABCD is a square. Points are chosen on each pair of adjacent sides of ABCD to form 4 congruent right triangles, as shown below. Each of these has one leg that is twice as long as the other leg. What fraction of the area of square ABCD is shaded? F. G. H. 1 J. 3 K. 9 A. B. C. D. E. Mr . Mosaad El Geneady Mo: 01001851053 ACT 35 Geometry Section (7) 1. What is the surface area, in square inches, of an 8-inch cube? 5. If a rectangle measure 54 meter by 72 meters, What is the length of the rectangle? F. 512 G. 384 H. 320 J. 256 K. 192 F. 48 G. 63 H. 90 J. 126 K. 252 2. Triangles _ABC and _PQR are shown below. The given side lengths are in centimeters. The area of ABC is 30 square centimeters. What is the area of PQR, in square centimeters? 6. Parallelogram ABCD, shown below. What its area? F. 15 G. 19 H. 25 J. 30 K. 33 3. Which of the following sets of triangle side lengths Represent a right triangle A. 1, 2, 5 B. 2, 3, 4 C. 4, 5, 21 D. 5, 12, 13 E. 6. 9. 11 4. In the figure below, ABCE is a square and E,F,G and H are the midpoints of its sides. If AB = 12cm what is the perimeter of EFGH ? A. 18 B. 36 C. 39 D. 45 E. 72 7. The trapezoid below is divided into 2 triangles and 1 rectangle. What is the combined area of the 2 shaded triangles? A. 4 B. 6 C. 9 D. 12 E. 18 8. Point B on ̅̅̅̅ between A and C. Point D is a point not on ̅̅̅̅ such that the measure of ABD is 38. What is the measure of CBD? F. 24 G. 24√ H. 36√ J. 48√ K. 72 Mr . Mosaad El Geneady A. 38 B. 52 C. 76 D. 128 E. 142 Mo: 01001851053 36 ACT 9. The tent illustrated below is in the shape of a right triangular prism and is made of nylon. How many square feet of nylon is required for the front, rear, and 2 sides of the tent? F. 47 G. 59 H. 82 J. 94 K. 188 10. In the rhombus ABCD below, ̅̅̅̅ is 8 inches long and ̅̅̅̅ is 6 inches long. What is the area of ACBD Geometry 12. What is the circumference of a circle with radius 6cm? F. G. H. J. K. 3 9 12 36 13. In the figure is below, parallel lines ⃡ and ⃡ are cut by transversals ⃡ and ⃡ that intersect at E. What is the measure of ABD ? F. 110 G. 112 H. 138 J. 144 K. 146 F. G. H. J. K. 5 24 25 32 48 11. In the figure is below, B,F, and H are on ̅̅̅̅ , ̅̅̅̅ , and ̅̅̅̅ , respectively, and ̅̅̅̅ ̅̅̅̅ . The area of square ABGF is the area of square ACDE. The the area of FGH is what fraction of the area of square ACDE. F. G. H. J. 14. The intersection of lines l and m forms the 4 angles A, B, C, and D. The measure of B is 3 times the measure of A. which of the following closest to measure A ? F. 20 G. 26 H. 35 J. 40 K. 51 15. In ABC shown below, sin C = and the length of ̅̅̅̅ is 10 inches. What is the length of ̅̅̅̅ ? A. 3 B. √ C. 8 D. 9 E. K. Mr . Mosaad El Geneady Mo: 01001851053 37 ACT 16. The length of the rectangular prism shown below is twice the width. The height and the width are the same. The volume of the prism is 128 cubic inches . what is the length of the prism? A. 2 B. 4 C. 8 D. 16 E. 32 17. Each edge of a cube is 4 inch long. Each edge of a second cube is triple the length of each edge of the first cube. The volume of the second cube is how many cubic inches bigger than the volume of the first cube ? F. 128 G. 512 H. 576 J. 1,664 K. 1,728 18. The midpoints of the sides of rectangle WXYZ are vertices of rhombus ABCD . The dimensions of rectangle WXYZ are 6cm by 8cm. What is the perimeter of rhombus ABCD ? F. G. H. J. K. 20 25 28 40 36 Geometry 20. In the figure is shown below, ̅̅̅̅ divides the rectangle ACDF into 2 congruent trapezoids. the measure of BED is 45, ̅̅̅̅ ̅̅̅̅ = 4cm length of ̅̅̅̅ = 6cm. What is the area of rectangle ACDF F. G. H. J. K. 20 25 28 40 36 21. In the figure below, p is on ̅̅̅̅, and E is on ̅̅̅̅ , polygon ABCDEF, with dimensions marked, has area of 122 square inches. What is the area of PEB ? F. 3 G. 6 H. 12 J. 13 K. 15 22. What is the length of side of square whose area is equal to area of a rectangle 25m by 16m ? 19. In trapezoid ABCD shown below, ̅̅̅̅ is 8cm , ̅̅̅̅ is 12cm long, and ̅̅̅̅ is 6 cm . AEF and DFE are right angles. What is the area of the trapezoid ? A. 60 B. 72 C. 84 D. 120 E. 288 Mr . Mosaad El Geneady A. √ B. 42 C. 48 D. 67 E. 71 Mo: 01001851053 38 ACT 23. What is the volume of right circular cylinder shown below ? F. G. H. J. K. 220 310 700 1,540 2,200 24. A swimming pool in the shape of a right rectangular prism has length 12 feet and width 14 feet. The volume of water in the pool is 2,520ft3. To nearest foot, what is the depth of water in the Pool? F. G. H. J. K. 7 10 15 24 90 25. In a certain rectangle, the ratio of the lengths of 2 adjacent sides is 5 to 2. If the area of the rectangle is 90 square inches, what is the length of the longest side? A. 6 B. 9 C. 15 D. 18 E. 45 Geometry 27. A formula for the surface area (A) of the rectangular solid shown below is A = 2lw + 2lh + 2wh where l represents length; w, width; and h, height. By doubling each of the dimensions (l, w, and h), the surface area will be multiplied by what factor? A. 02 B. 04 C. 06 D. 08 E. 12 28. The triangle, XYZ, that is shown below has side lengths of x, y, and z inches and is not a right triangle. Let X` be the image of X when the triangle is reflected across ̅̅̅̅. Which of the following is an expression for the perimeter, in inches, of quadrilateral X`YXZ ? F. 2(y + z) + x G. 2(x + y + z) H. 2(x + y) J. 2(x + z) K. 2(y + z) 29. A pyramid composed of 4 congruent triangular sides and a square base is shown “unfolded” in the standard (x,y) coordinate plane below. Points A, B, and C are vertices of 1 of the triangular sides. What is the total surface area of the pyramid? 26. A computer chip 0.32 cm thick is made up of layers of silicon. If the top and bottom layers are each 0.03 cm thick and the inner layers are each 0.02 cm thick, how many inner layers are there? A. 13 B. 15 C. 16 D. 52 E. 64 Mr . Mosaad El Geneady F. 240 G. 2√ H. 9 J. 20 K. 400 Mo: 01001851053 39 ACT 30.What is the area, in square inches, of the figure below? Geometry 33. The perimeter of a particular rectangle is 36 cm. The longer sides of the rectangle are each 2 cm longer than each of the shorter sides of the rectangle . What is the length of one of the longer sides of this rectangle ? A. 8 B. 9 C. 10 D. 18 E. 32 A. 4 B B. 6 C. 8 D. 9 10 A E. 11 3 5 31. Rhombus RHOM e is shown below, If HR = 5m, HM = 6m, then what is length of ̅̅̅̅ A. 3 B. 4 C. 5 D. 6 E. 8 32. In the figure is shown below, A right square pyramid with equilateral triangular faces . The slant height of the pyramid is 3√ inches. What is the total length of all 8 edges of the pyramid? 34. What is the length of diagonal of the rectangular solid shown in the figure above? A. B. C. D. E. 11.18 11.58 14.18 15.44 20.18 35. If the volume of a cone is 24 cubic feet and its height is 2 feet, what is the diameter of the base A. 3 B. 6 C. 12 D. 24 E. 36 36. The right circular cylinder in the figure above has height 3 inches and volume 48 cubic inches, and segment AC is a diameter of the base. What is the area, in square inches, of triangle ABC ? F. G. H. J. K. 12 21 24 36 48• Mr . Mosaad El Geneady A. 6 B. 8 C. 12 D. 16 E. 24 Mo: 01001851053 ACT Section (8) 1. A chord 24 inches long is 5 inches from the center of a circle, as shown below. What is the radius, to nearest tenth of an inch? 40 Geometry 4. Points A through F lie on the circle shown below so that the distance between any 2 adjacent points is equal. The circle has a diameter inches. What is the length of ̅̅̅̅? A. B. C. 3 D. √ E. A. 29.0 B. 24.5 C. 16.9 D. 13.0 E. 10.9 2. Points A and B lie on the circle below, where Central angle ACB measure 110. What is the measure ABC? F. 35 G. 40 H. 45 J. 55 K. Cannot be determined from the given information 3. In the figure below, ̅̅̅̅ and ̅̅̅̅ are tangent to the circle at B and C, and O is the center of the circle If the measure of BAC is 40, What is the measure of AOB ? 5. In the circle below, O is the center. Chord ̅̅̅̅ is 12 inches long and 8 inches from O. What is the Area of the circle? F. 36π G. 64π H. 80π J. 100π K. 208π 6. A circle with center C is shown below. Points W, Z, Y, and Z lie on the circle. The measure of WCY is 100, the measure of XCZ is 80, the measure of WCZ is 150, What is the measure of XCY? A. 20° B. 25° C. 30° D. 40° E. 50° 7. The circumference of a circle is 50 cm. What Is its diameter ? F. 40 G. 50 H. 60 J. 70 K. 80 Mr . Mosaad El Geneady F. G. H. 50 J. 25 K. 50 Mo: 01001851053 ACT 8. In the shown below, ̅̅̅̅ is 15 inches long, chord ̅̅̅̅ is 10 inches long, and ̅̅̅̅ is perpendicular to ̅̅̅̅ at D. How many inches long is ̅̅̅̅? 41 Geometry 12. A right circular cylinder is shown in the figure below, with dimensions given in centimeters. What is the total surface area of this cylinder, in square centimeters? (Note: The total surface area of a cylinder is given by 2r2 + 2rh where r is the radius and h is the height.) A. 10 B. 15 C. 5√ D. 5√ E. 10√ 9. A circle with center C is shown below. Points W, Z, Y, and Z lie on the circle. The measure of WCY is 100, the measure of XCZ is 80, the measure of WCZ is 150, What is the measure of XCY? A. 20° B. 25° C. 30° D. 40° E. 50° 10. The circumference of a circle is 50 cm. What Is its diameter ? F. G. H. 50 J. 25 K. 50 11. If the measure of one angle of a rhombus is 120and its perimeter is 16 cm, then what is the length of its longer diagonal? A. 4 B. √ C. √ D. √ E. √ Mr . Mosaad El Geneady A. 300 B. 400 C. 500 D. 600 E. 1,600 13. The track for a model railroad display is set up 2 circles that are tangent to one another and have diameters of 30 feet and 50 feet respectively as shown below. The engine of the train travels at a constant rate of 75 feet per minute. To the nearest minutes, how many minutes does the engine take to go in a figure 8 pattern around the entire exactly 1 time? F. G. H. J. K. 1 2 3 4 7 14. What is the length of the edge of a cube having the same total surface area as a rectangular prism measuring 3 cm by 4 cm by 8 cm? A. 22.7 cm B. 4.8 cm C. 136 cm D. 5.8 cm E. 11.7 cm Mo: 01001851053 42 ACT 15. The circle below has a diameter of 8 cm. Which of the following is closest to the area of the square inscribed in the circle? Geometry 16. Pablo has a deck and pool in his backyard. The Deck`s shape is a rectangle with a semicircle removed and is shown shaded in the figure below The lengths of the straight sides of the deck are given in feet. Pablo plans to cover the top of the deck with stain. To decide how much stain to purchase, he needs to find the area of the top of the deck. To the nearest square foot, what is the area of the top the deck? A. 25 B. 32 C. 50 D. 64 E. 201 16. A can of soda pop has the shape of a right circular cylinder with an inside height of 6 inches and an inside diameter of 2 inches. When you pour the soda pop from the full can into a cylindrical glass with an inside diameter of 3 inches, about how many inches high is the soda Pop in the glass? ( Note: The volume of right circular cylinder is r2h) F. G. H. J. K. 2 4 5 6 8 F. G. H. J. K. 110 226 238 332 414 17. In the figure below points E, F,G, and H are on The sides of square ABCD. arc ̂ has center at A ̂ at B, ̂ at C, and ̂ at D. All of the arcs have a radius of 3 feet. What is the area of the shaded region? 41. What is the volume of a sphere whose surface area is 100π cm2? A. cm3 B. cm3 C. 160π cm3 D. cm3 E. 520 cm3 Mr . Mosaad El Geneady A. B. C. D. E. Mo: 01001851053 ACT 18. Secant AC and CE intersect at C, The chord AB and DE are congruent , Minor arc ̂ measure 106. Minor arc ̂ measure 64. What is the measure of arc ̂ 43 Geometry 21. 2 circular pulleys with centers 8 inches apart are connected with a tight belt. The belt warps of the way around the large pulley, which has radius of 5 inches, and of the way around the small pulley, which has radius of 1 inch. What is the exact length of the belt, in inches? F. 42 G. 84 H. 85 J. 90 K. 95 19 . Graphed in the standard(x,y) coordinate plane below is line l and the circle with equation (x – 2 )2 + y2 = 1. Line l passes through O(0, 0) and is tangent to the circle at A, and B is the center of the circle. What is the measure of AOB? F. 15 G. 22.5 H. 30 J. 45 K. 60 20. A circle, 2 chords, are shown in the figure is shown below, what is the value of x ? F. G. H. J. K. √ √ √ 22. A small circle and a large circle are tangent at T, as shown below. The center of the large circle lies on the small circle. The diameter of the large circle is 12 cm. What is the ratio of the area of the small circle to the area of the large circle? A. B. C. D. E. A. 10 B. 13.5 C. 14 D. 17.5 E. 19 Mr . Mosaad El Geneady Mo: 01001851053 ACT 23. The circle shown below had diameter ̅̅̅̅, and points B and C lie on the circle. The measure of CAD is 30, and the measure of minor arc ̂ is 60. What is the measure of minor arc ̂ ? 44 Geometry 26. The figure shown below is composed of a rectangle and a semicircle. Points A and B are endpoints of both a side of the rectangle and a diameter of the semicircle. What is the perimeter, in feet, of the figure? F. 72 G. 98 H. 100 J. 108 K. 116 24. In the circle shown below, chords and intersect at P, which is the center of the circle, and the measure ofPST is 30°. What is the degree measure of minor arc ̂ ? F. 30° G. 45° H. 60° J. 90° K. Cannot be determined from the given information 25. In the circle shown below, M is the center and lies on ̅̅̅̅ and ̅̅̅̅ . Which of the following statements is NOT true? F. TUM measures 65° G. ̅̅̅̅ .is parallel to ̅̅̅̅ H. ̂ measures 50° J. ̅̅̅̅̅ ̅̅̅̅̅ K. ̅̅̅̅ ̅̅̅̅ Mr . Mosaad El Geneady F. 3 + 20 G. 3 + 22 H. 6 + 14 J. 6 + 24 K. 9 + 48 27. The figure below consists of a square and 2 semicircles, with dimensions as shown. What is the outside perimeter, in centimeters, of the figure? A. 8 + 8π B. 16 + 8π C. 16 + 16π D. 32 + 8π E. 32 + 16π 28. The diameter of one circle is 12 inches long. The diameter of a second circle is 25%longer than the diameter of the first circle. To the nearest square inch, how much larger is the area of the second circle than the area of the first circle? F. 7 G. 28 H. 44 J. 64 K. 254 Mo: 01001851053 ACT 29. An 8-foot-square sheet of tin from which 4 identical circles are cut is shown below. Each circle is tangent to 2 other circles and tangent to 2 of the edges of the square. What is the approximate area of the remaining tin as indicated by shaded region below? A. 51.4 B. 38.9 C. 19.4 D. 13.7 E. 6.9 45 Geometry 32. A chord 24 inches long is 5 inches from the center of a circle. What is the radius of the the circle to nearest tenth of an inch? A. 29.0 B. 24.5 C. 16.9 D. 13.0 E. 10.9 33. In the figure below, 2 tangent circles such that the 10-centimeter diameter of the smaller circle is equal to the radius of the larger circle. What is the area of the shaded part? 30. Two concentric circles are shown below. The radius of the larger circle is 10 feet and the radius of the smaller circle is 6 feet. What is the area of the shaded region bounded by the circles? F. 8 G. 16 H. 36 J. 64 K. 100 31. The diagonal of a square is 12. What is the length of a side? A. √ B. 14.1 C. 8.5 D. 6.9 E. 17 Mr . Mosaad El Geneady F. 10 G. 75 H. 5π J. 10π K. 75π 34. A 6-inch-by-8-inch rectangle is inscribed in a circle as shown below. what is the area of the circle, in square inches? F. 5π G. 16π H. 25π J. 48π K. 96π Mo: 01001851053 46 ACT 35. In the figure below, AB BC, and ̅̅̅̅ is a diameter of the circle, having a length of 4 cm. what is the area of ABC ? Geometry 38. The circumference of a circle is 20 cm. What is length of the radius of the circle? A. B. F. G. H. J. K. 2 4 8 √ 4√ C. D. 20 E. 20 36. As shown in the figure below, D is the center of the circle, and right triangle ABD intersect the circle at C and F. Point C is the midpoint of ̅̅̅̅, 12 cm long. The shaded region inside the circle and outside the triangle has an area 32. What is the measure of A? F. 40 G. 45 H. 50• J. 58• K. 67.5• 37. The large with radius R inches is shown below; 3 small nonoverlapping circles, each with radius r inches, are removed from the large circle. remaining after the 3 circles were removed. What is the area of the shaded region? A. r2 B. R2 C. R2 – r2 D. R2 – 2r2 E. R2 – 3r2 Mr . Mosaad El Geneady 39. In the figure above, points A, B, C and D lie on the circle. If the measure of arc ̂ is 160°, what is the value of x ? A. B. C. D. E. 16 20 32 40 64 40. What is the circumference of a circle whose area is 64π cm2? A. 16 B. 8π C. 8 D. 128π E. 16π 41. The circumference of a circle is 12 inches. What is the area of the circle? A. 4 B. 9 C. 12 D. 16 E. 36 Mo: 01001851053