Chapter 4 Review Formal Geometry Name: Period: Due on the day of your test:
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1 Multiple Choice Identif the choice that best completes the statement or answers the question. 1. In the figure, what is the m 3?. 97 B C In the figure, PR SU and QT QU. What is the measure of STQ? U. 30 B. 120 C. 150 S T R Q 3. In the figure, l and m are parallel and m 1 = 67 and m 2 = 36. What is the 3? P. 103 B. 89 C l m 1
2 4. In a coordinate proof, which of the following would be most useful to prove that triangles are congruent b SSS Triangle Congruence Theorem?. distance formula B. midpoint formula C. corresponding parts of congruent triangles are congruent (CPCTC). slope formula 5. Given BC with vertices at (5, 2), B(7,2), C(3, 5), what is the classification of the triangle b its sides?. equilateral B. scalene C. isosceles. equiangular 6. In the figure, GE L and E. What information is needed to prove that GE L b SS? G. GE L L B. G L C. GE L E. EG L 2
3 7. In the figure H L and HJ = JL. Which of the following statements about congruence is true? I. HIJ LKJ b S K B. HIJ KLJ b SSS C. HIJ KLJ b SS. HIJ LKJ b SS J H L 8. Refer to the figure to complete the congruence statement, BC.. CE B B. EC C. E C. E E 9. Given the figure, what theorem can be used to conclude that CB CE?. S B. SS C. SSS B C E. 3
4 10. etermine which postulate or theorem can be used to prove the pair of triangles congruent.. S B. SS C. S. SSS 11. Given EF LMN, m = ( + 75), m L = (3 + 15), and F = 2 26, what is the length of F?. 28 B. 34 C In the figure, BC F. What is the m?. m = 1 B. m = 7 C. m = 42. m = 60 B +4 C (6) 2-3 F 4
5 13. In the figure, MN NPM. What is the value of? M (5+12). 8 B. 10 C P (5+2) N 14. The picture shows a drawing of a boat. What is the m 3?.. m 3 = 128 B. m 3 = 119 C. m 3 = 52. m 3 = Given MNP, nna is proving m 1 + m 2 = m 4. Which statement should be part of her proof? N. m 3 + m 4 = B. m 1 = m 3 C. m 1 + m 3 = 180. m 1 = m 2 M P 5
6 Given: Prove: Q is the midpoint of MN ; MQP NQP. MQP NQP M Q N P Statements Reasons Q is the midpoint of MN 16. If a point is the midpoint of a segment, then 2 segments are created. MQP NQP QP QP MQP NQP 17. Fill in the proof above and choose the best answers for 15 and Choose one of the following to complete the proof.. MQ = NQ B. MQ NQ C. MP NP. QP QP 17. Choose one of the following to complete the proof.. Refleive propert of equalit B. Linear pair Theorem C. SS Congruence. S Congruence 6
7 18. Position and label the triangle on the coordinate plane. right with hpotenuse, leg 4a units long, and leg one-fourth the other leg a. c. B (0, 4 a) C (0, a) B (0, 0) (4 a, 0) ( a, 0) C (0, 0) b. d. C (0, 4 a) B (0, a) B ( a, 0) (0, 0) C (0, 0) (4 a, 0) 19. Triangles MNP and MN are congruent equilateral triangles. Find and M (3 + 6) + 4 P N a. c. b. d
8 21. Identif the tpe of congruence transformation. a. reflection c. not a congruence transformation b. translation d. rotation Identif the tpe of congruence transformation. 22. a. reflection onl c. rotation or translation b. not a congruence transformation d. rotation onl 8
9 23. Circle the choice where the triangle is positioned and labeled correctl. Isosceles with base 2b units long a. c. M ( b, c) L(0, 2 b) N ( c, b) L (0, 0) N (2 b, 0) M(0, 0) b. d. L ( b, c) N (0, 2 b) L ( c, b) M(0, 0) N (2 b, 0) M(0, 0) 24. Find, PQ, QR and RP if PQR is an isosceles triangle with PQ QR.. = 8, PQ = 17, QR = 9, RP = 16 B. = 9, PQ = 19, QR = 19, RP = 10 C. = 4.5, PQ = 10, QR = 5.5, RP = 5.5. = 0, PQ = 1, QR = -8, RP = 1 9
10 25. Name the congruence transformation. F F'. Reflection B. Glide Reflection C. Translation. Rotation H G H' G' 26. Find the measure of the sides of with vertices at and Choose the best classification of the triangle b its sides. Hint: Use the distance formula!. Equilateral B. Isosceles C. Scalene. None of the bove (on t pick this choice!) 27. In the figure, m BC = m CB =. Find the m CB in terms of. E B C C B 10
11 Write a two-column proof for the following problems: You will have 3 proofs on the test. 28. Given: W is the midpoint of and. Prove: X V W Z Y 29. Given: is isosceles with base ; ;. Prove: F G H I 30. Given: Prove: B C 11
12 31. Given: C is the midpoint of BF; and are right angles. Prove: B C F G 32. Given: Prove: B P Q C
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