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# 1. S T V [A] VT [C] VT U Which of the following best describes what SVT and TVU have in common? A [B] VT [D] V, T #2. B C D E O A Which of the following is a pair of supplementary F angles? [A] BOF and BOA [B] COD and DOE [C] COF and AOF [D] DOE and DOB D #3. A F B C D E Q Which two angles are adjacent? N M S J K G TU H I C [A] BMD and KMS [B] MKT and NJT [C] FJG and NJF [D] DEQ and TIG #4. Plane P contains points A, B, and C. A different plane, plane Q, contains points B, C, and D. Which of the following represents the intersection of P and Q? B [A] AD [B] BC [C] BC [D] points B, C, A, and D #7. E(3, 4, - 5) F(- 6, 10, 0) What are the coordinates of the midpoint of EF? B [A] (4.5, 7, 2.5) [B] (- 1.5, 7, - 2.5) [C] (4.5, 3, - 2.5) [D] (- 1.5, 3, - 2.5) #8. What is the approximate distance between the points (- 13, 8) and (206, 196) in the xy-plane? C [A] 219 units [B] 269 units [C] 289 units [D] 299 units Mt. Lookout (78,71) Using the map, the #9. highway department locates two exits between Exit 2 Tomstown and Mount Lookout. From Exit 1 Tomstown, Exit 1 is halfway to Mount Lookout, and Exit 2 is Tomstown (2, 3) three-fourths of the way to Mount Lookout. What are the coordinates for Exit 2? [A] (74, 37) [B] (59, 54) [C] (40, 37) [D] (68, 54) B #10. In the xy-plane, (-3, 1) and (4, 3) are endpoints of a diameter of a circle. What are the coordinates of the center of the circle? 1 [A] ( ,2) 2 [C] (1,4) 7 [B] ( ,1) 2 7 [D] (- ,-1) 2 A #11. (12, 9) (0,8) (12, 3) (0,2) The county planning department designs a new park in the shape of a parallelogram. They put in two diagonal walkways. What will be the coordinates of the intersection of the diagonal walkways? [A] (6, 2.5) [C] (5.5, 6) [B] (5, 6.5) [D] (6, 5.5) D #12. 3 1 2 Given: m1 = 4 x, m 2 = (3 x + 10), and m 3 = (2 x + 17). What is m 2? [B] 47 [A] 61 [C] 31 [D] 17 A #13. A B If ABCD is a 1 rhombus and m ABC = 80, what is the measure of 1? C D [A] 40 [C] 80 A [B] 50 [D] 90 #14. ABCD is a parallelogram. If m BCD = (6 x – 20) and m DAB = (2 x + 80), what is the value of x? [A] 8.3 [C] 15 D [B] 12.5 [D] 25 #15. 12 in. N M Which of the following statements 25 in. about the picture is true? O B [A] mO > mM [B] mM > mN [C] mM < mN [D] mN < mO #16. Write the following statement in “If-then” B “Two angles that form a linear pair are form. supplementary.” [A] If two angles are supplementary, then they form a linear pair. [B] If two angles form a linear pair, then they are supplementary. [C] If two angles are not supplementary, then they form a linear pair. [D] If two angles do not form a linear pair, then they are supplementary. #17. What is the inverse of the statement below? If a triangle is scalene, then no two angles are congruent. [A] If the triangle is not scalene, then there are [B] [C] [D] two congruent angles. If two angles of a triangle are congruent, then the triangle is scalene. If there are two congruent angles in a triangle, then the triangle is not scalene. If the triangle is not scalene, then there are no congruent angles. A #18. What is the contrapositive ofthe statement below? If a triangle is isosceles, then it has two congruent sides. [A] If the triangle does not have two congruent sides, then it is not isosceles. [B] If a triangle has two congruent sides, then it is isosceles. [C] [D] A If a triangle is isosceles, then it has two congruent sides. A triangle has two congruent sides if and only if it is isosceles. #19. The conditional statement “All 45° angles are acute angles” is true. Based on the conditional statement, which of the following can be concluded from the additional statement “The measure of A is 45°”? [A] A is an acute angle. [B] A is not an acute angle. A [C] The complement of A is not an acute angle. [D] The supplement of A is not an acute angle. #20. n m k 1 2 t 3 If k | | m | | n, Which of the statements justifies the conclusion that 1 2 3? D [A] then alternate interior angles are congruent. [B] then vertical angles are congruent. [C] then alternate exterior angles are congruent. [D] then corresponding angles are congruent. A #21. C B D It is given that AC AD andCAB DAB. By the reflexive property of congruent segments, AB AB. Which reason could be used to prove Δ ABC Δ ABD? [A] side-angle-side [C] side-side-side A [B] hypotenuse-leg [D] angle-side-angle #22. A D M B C Given: ABCD is an isosceles trapezoid. M is the midpoint of AB. Prove: DM CM #22. M is the midpoint of AB. AM MB Def of midpoint given ? ABCD is an isosceles trap. given ΔADM Δ BCM DM CM AD BC Def isos.trap. CPCTC #22. [A] What is the missing statement and reason that completes the proof? B AD BC; the legs of an isosceles trapezoid are congruent. MBC; the base angles [B] MAD of an isos. trap. are congruent [C] AM BM; corresponding parts of congruent triangles are congruent [D] ABC DAB; if lines are parallel, s-s int.angles are supp. #23. X A Given: Δ ABC B Y C Prove: m BAC + m ABC + m BCA = 180 #23. STATEMENTS 1) Draw XY through B and parallel to AC. REASONS 1) Exactly one parallel line can be drawn to given line from pt. not on line. 2) XBA and ABY form a linear pair. 2) Definition of a linear pair 3) m XBA + m ABY = 180 3) The sum of the measures of the angles of a linear pair is 180. 4) m ABC + m CBY = m ABY 4) Angle Addition Postulate 5) m XBA + m ABC + m CBY = 180 5) Substitution 6) CBY BCA and XBA BAC 6) ____________________________ 7) m CBY = m BCA and m XBA = m BAC 7) Definition of congruent angles 8) m BAC + m ABC + m BCA = 180 8) Substitution #23. [A] [B] What is the reason for statement 6 in the proof? A Alternate interior angles of parallel lines are congruent. Alternate exterior angles of parallel lines are congruent. [C] Vertical angles of parallel lines are congruent. [D] Corresponding angles of parallel lines are congruent. #24. What is the measure of angle y? D [A] 40 40° [B] 60 x 60° y [C] 80 [D] 100 #25. B BD is the angle bisector of ABC. If m A = m C = 50, what is m ABD? A D C [A] 30 [B] 40 [C] 45 [D] 50 B #26. OB bisects AOC. If m AOB = (3 x + 16) and m BOC = (8 x – 14), what is m AOB? [A] 18 [C] 34 [B] 26 C [D] 48 #27. c 1 2 a 3 4 b [A] Line [B] Line [C] Line [D] Line 1 is supplementary to 3 under which of the following conditions? A a is parallel to line b. a is parallel to line c. a is perpendicular to line c. b is perpendicular to line c. #28. For which type of convex polygon is the sum of the measures of the interior angles equal to the sum of the measures of the exterior angles, one at each vertex? D [A] triangle [B] hexagon [C] pentagon [D] quadrilateral #29. Q R If m P = 120º, what is the sum of the measures of the remaining S interior angles? C P 120° [A] 240 [B] 360 U T [C] 600 [D] 720 #30. The measure of each exterior angle of a regular polygon is 45. How many sides does the polygon have? [A] 4 [B] 5 [C] 8 [D] 9 C #36. An isosceles triangle has vertices at (1,1) and (3, 3). Which of the following could be the coordinates of the third vertex? [A] (2, 1) [C] (4, 1) D [B] (3, 2) [D] (5, 1) #37. Triangle MNO has vertices with coordinates M (0, 2), N (1, 0), and O (5, 1). What type of triangle is Δ MNO? [A] isosceles [B] right [C] scalene C [D] equilateral #38. In triangle XYZ, W is between Y and Z. The coordinates are X (2, 3), Y (5, 0), Z (0, 0), and W (2, 0). What is XW? A [A] altitude [B] angle bisector [C] median [D] perpendicular bisector of the side #39. What is the most specific name for quadrilateral ABCD with vertices A (0, 0), B (3, 4), C (6, 0), and D (3, - 4)? C [A] parallelogram [B] rectangle [C] rhombus [D] trapezoid #40. In rectangle ABCD, diagonal AC = (3 x – 9) and diagonal BD = (x + 13). What is AC? [A] 16 [C] 24 C [B] 18 [D] 32 #41. In parallelogram RSTU, the diagonals intersect at E. If RE = 10 and SU = 16, what is RT? [A] 20 [B] 16 [C] 10 [D] 8 A #42. B A C If points A, B, C, and D form a trapezoid, how many ordered pairs could represent D? D [A] 1 [B] 2 [C] 3 [D] an infinite number #43. 13 A x-5 12 E D B F C 2x - 1 [A] 5 units [C] 9 units ABCD is a trapezoid with 15 median EF. What is the length of AB? A [B] 7 units [D] 10 units #45. If the sides of a triangle are 3, 7, and x, which of the following best describes x? [A] 4 < x < 10 [C] x < 10 [B] 4 ≤ x ≤ 10 A [D] x>4 #46. C X A Y B [A] 36 [B] 41 [C] 67 [D] 72 In Δ ABC, X is the midpoint of AC and Y is the midpoint of BC. If m C = 67 and m A = 72, what is m CYX? B #48. A triangle has interior angles that measure 3 x, (2 x + 15), and (x + 45). What is the measure of the largest exterior angle? [A] 160 [B] 125 [C] 120 [D] 115 B #49. B Y A Z In Δ ABC, Z is the midpoint of AC and Y is the midpoint of BC. If YZ = 21 and C AB = (2 x – 4), what is x? [A] 7.25 [B] 12.5 [C] 23 [D] 46 C #69. Given points P (7, 5), Q (8, 3), R (0, - 1), and (- 1, 1), which of the following is true?A [A] PQ is parallel to RS. [B] PQ is perpendicular to RS. [C] PR is perpendicular to QS. [D] PR is parallel to QS. #70. Which is an equation of a line parallel to: 2 1 - x+ y = 4 3 5 [A] - 10x + 3y = 6 [B] - 3x + 10y = 6 [C] 3x - 10y = - 6 [D] 10x + 3y = - 6 A #71. What is the slope of the line that is perpendicular to the line whose equation is: 3x-2y=-8 3 [A] 2 2 [B] 3 2 [C] 3 3 [D] 2 C #72. ABCD is a rhombus. The slope of AB is 3/8. What is the slope of DC? 8 [A] 3 3 [B] 8 3 [C] 8 8 [D] 3 B #73. Which of the following is an equation of the line perpendicular to: 3x + 6y = 12 at (4,0)? 1 1 [B] y = x - 2 [A] y = - x + 2 2 2 [C] y = - 2x + 8 [D] y = 2x - 8 D #74. P k 1 [A] y = - x 3 [C] y = - 3x - 8 Line k contains point P and the origin. Which is an equation of the line that is perpendicular to line k and passes through point P? D 1 [B] y = x + 2 3 [D] y = 3x + 10