Geometry Exam 3 Review 1. Circle the triangles that can be proven to be congruent and state how you know they are congruent. a. b. c. d. 2. True or false (To be true, it must always be true): a. If two angles share a common vertex, then they must be adjacent angles. b. If a quadrilateral has all four angles congruent, then the quadrilateral must be a square. c. If two lines cut by a transversal form a pair of supplementary interior angles on the same side of the transversal, then the lines must be parallel. d. If two sides and any one angle of one triangle are congruent to two sides and any one side of another triangle, then the triangles must be congruent. 3. B C R A Given: isosceles trapezoid ABCD, isosceles triangles BRC and ARD If BRA 80 and < BCD = 100 find the measures of < CDA and < BAR D 4. Use a compass and straight edge to construct a 60 degree angle. 5. Use a compass and straight edge to construct a 45 degree angle. 6. Use a compass and a straight edge to construct a right isosceles triangle with legs of length a. a 7. Use a compass and straight edge to construct a triangle given two sides of lengths a and b, and their included angle C. (Note: you must reconstruct angle C.) a b C 8. 1 2 3 4 5 6 Given: the figure <7 = 100 <9 = 50 7 8 11 12 9 10 13 14 a. Name a pair of vertical angles ___________________________________ b. Name a pair of corresponding angles______________________________ c. Name a pair of alternate interior angles_____________________________ d. Name a pair of alternate exterior angles_____________________________ e. Name a pair of interior angles on the same side of the transversal______________________ f. Name a pair of exterior angles on the same side of the transversal______________________ g. <4 = _______________________ h. <8 = ________________________ i. <12 =_______________________ j. <3 = ________________________ k. < 6 = ________________________ l. < 5 = ________________________ m. < 2 = ________________________ 9. A B C In ACD, AD CD , ADB CDB , AC=16 cm, AD = 20 cm and ADB = 24 Round to the nearest hundredth if needed. a. How long is BC ? D b. How long is BD ? c. What is the measure of DAB 10. Given isosceles trapezoid ABCD with AB CD , prove that ABD DCA B C A D 11. A B Given that C is the midpoint of both AE and BD , prove that A E C D E 12. Find the measures of all of the angles of the following parallelogram. 2x+25 x 10 13. Use the given figure to calculate the numbered angles given that m n 1 2 45 3 m n 5 70 4 6 14. B 20m C 30 In the parallelogram ABCD, find the height. Then calculate the area of ABCD. 18 m A D Answers: 1.a. not 1.b. by SSS or SAS 1.c. by HA, AAS or ASA 1.d. not 2.a. False 2.b. False 2.c. True 2.d. False 3. CDA = 80, BAR = 40 4. - 7. See below 8.a. through f. more than one answer is possible. Example answers are given. 8.a. 1 and 6 8.b. 6 and 14 8.c. 6 and 9 8.d. 3 and 11 8.e. 6 and 10 8.f. 1 and 13 8.g. 80 8.h.80 8.i. 100 8.j.80 8.k.50 8.l.50 8.m. 50 9.a. 8 cm 9.b. 18.33 cm 9.c. 66 10. Statement Reason 11. Statement Reason 1. AB CD 1. Given 1.C is midpoint of AE and BD 1. Given 2. BAD CDA 2. Given 2. AC EC and DC BC 2. Def. of midpoint 3. AD AD 4. ABD DCA 3. Reflexive 4. SAS 3. ACD ECB 4. ACD ECB 5. A E 3. Vertical angles 4. SAS 5. CP 12. two angles are 45 and two angles are 135 2 13. 1 70, 2 65, 3 65, 4=110, 5=135, 6=55 14. Height = 9m Area = 180 m