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Geometry Name _______________________________ Chapter 5 pretest Show work to receive credit! Date ______________________ Per. ______ It is given that Δ BCD is isosceles with base BD , m BCD = 78 , m QBD = 40 , CR bisects BCD, and BQ is an altitude. Find the measures of angles 1 through 6. B m 1 = _____ m 2 = _____ m 3 = _____ m 4 = _____ m 5 = _____ m 6 = _____ C 2 3 R 6 1 A Q 5 4 D 7. If CR is a median, BR = 2x – 5, and BD = 3x + 8, find RD. 8. Find the value of x and y so that the triangles are congruent by the indicated reason. ΔPQR ΔVSR by HA P V 8x - 35 2x - 5 5y Q 3y + 8 S R For problems 9 through 11, use the figure to the right to find each value. C 9. Name the shortest side of BCD . 60 D 50 80 10. Name the shortest side of ΔABD . 11. Name the shortest segment in 70 figure ABCD. 60 A 40 9. ________________ 10. ________________ 11. ________________ B For problems 12 through 15, identify the property that justifies each statement. 12. If m Y m G, then m Y > m G. 12. ______________________ 13. If x < 15, then 5 + x < 20. 13. ______________________ 14. If PQ > RS and RS > 12, then PQ > 12. 14. ______________________ 15. If -3x > 12, then x < 4. 15. ______________________ Given A(–5,1), B(–1,4), and C(2,-3) 16. Find the slope of each side. 17. Is ABC a right triangle? 18. Find the length of each side. 19. Classify ABC by its sides. 20. The perimeter ABC of is 84 cm. If AB = 8x – 3, BC = 2x + 12, and AC = 5x, find x and use it to find the lengths of each side. Use these measures to list the angles in order from largest to smallest. 20. ____________________________ 21. Complete the indirect proof below: Statement: If BD is not the angle bisector of ABC, then m 1 m 2. B Given: BD is not the angle bisector of ABC Prove: m 1 m 2 1 2 Assume: _______________________ Work: A D C This contradicts _______________________ Therefore, _______________________ is false, so _______________________ must be true. 22. Two sides of a triangle measure 37 and 19 inches. What is the range of values for the third side? 23. Which set of numbers below could be the lengths of the sides of a triangle? Justify your answers. a) 1,5,6 b) 16,35,18 c) 17,5,14 For problems 24 through 26, name the congruent triangles and state why they are congruent. Use a regular triangle rule (SSS, SAS, ASA, or AAS), then use a right triangle rule (LL, LA, HA, or HL). B C 24. 25. 26. B C 1 B A D AD CD D A ____________________ _________ _________ AD CD ____________________ _________ _________ For problems 27 and 28, write a two-column proof. 27. 28. G H Given: GF GE Prove: 1 E ____________________ _________ _________ G 1 1 F 2 A D 1 and 2 are right angles AD BC E C E F H Given: GE > GF Prove: 1 E E