IB MYP Unit 6 Review

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1 Name: Date: 1. Two triangles are congruent if 1. A. corresponding angles are congruent B. corresponding sides and corresponding angles are congruent C. the angles in each triangle have a sum of 180 D. corresponding sides are proportional 2. In the diagram below, ABC = XYZ. 2. Which two statements identify corresponding congruent parts for these triangles? 3. In the accompanying diagram, E is the midpoint of AB and CD. 3. Triangle AEC can be proved congruent to triangle BED by page 1

2 4. Given: BCG is isosceles, BG = CG, AB = CD, EC = FB 4. Prove: m E = m F Which triangle congruence case is required for the proof? A. ASA B. SAS C. SSA D. SSS Determine the length of ST if MN is (8x 3) units. page 2

3 6. In the diagram below of ABC, D is the midpoint of AB, and E is the midpoint of BC. 6. If AC = 4x + 10, which expression represents DE? 7. In the accompanying diagram, B is the midpoint of AC, DA AC, EC AC, and DB = EB. Which method of proof may be used to prove DAB = ECB? 7. A. SAS = SAS B. ASA = ASA C. HL = HL D. AAS = AAS 8. If two angles of one triangle are congruent to two angles of of another triangle, these triangles must be 8. A. similar B. congruent C. scalene D. isosceles page 3

4 9. In ABC, A = C, AB = 10x 7, BC = 2x + 33, and AC = 4x 6. Find x In the accompanying diagram of triangles BAT and FLU, B = F and BA = FL. 10. Which statement is needed to prove BAT = FLU? 11. In the accompanying diagram of quadrilateral QRST, RS = ST, SR QR, and ST QT. Which method of proof may be used to prove QRS = QTS? The measures of the angles of a triangle are represented by 4x, x + 40, and 2x. Find the value of x. 12. page 4

5 13. B and G are midpoints of AD and AE, and C and F are midpoints of BD and GE. If BG = 9, find the length of CF In the accompanying diagram, ACE, BCD, AB, and DE, A = E, and C is the midpoint of AE. Which theorem justifies ABC = EDC? 14. page 5

6 15. As shown in the diagram below, AC bisects BAD and B = D. 15. Which method could be used to prove ABC = ADC? 16. In the accompanying diagram of ABC, side AB is extended to D. If m ACB = x + 30, m CAB = 2x + 10, and m CBD = 4x + 30, what is the value of x? 16. page 6

7 17. Given: CF = EF FD is a median of CFE Prove: FD bisects CFE 17. statement reason FD is a median of CFE (1) CD = ED (2) (3) given (4) (5) CFD = EFD (6) (7) (8) FD bisects CFE (9) In the above proof, what is reason (6)? 18. In the diagram of ABC and EDC below, AE and BD intersect at C, and CAB = CED. 18. Which method can be used to show that ABC must be similar to EDC? page 7

8 19. In the diagram below, ABC EFG, m C = 4x + 30, and m G = 5x Determine the value of x The diagram below shows the construction of the bisector of ABC. Which reason for triangle congruence is used in proving that BF bisects ABC? 20. A. ASA B. SAS C. SSS D. SAA page 8

9 21. Given: Prove: WY is the angle bisector of XWZ m XYW = m ZYW WXY = WZY 21. statement reason WY is the bisector of XWZ (1) m XWY = m ZWY (2) WY = WY (3) m XYW = m ZYW (4) WXY = WZY (5) In the above proof, what is reason (3)? 22. In the accompanying diagram, RL LP, LR RT, and M is the midpoint of TP. Which method could be used to prove TMR = PML? 22. A. SAS = SAS B. AAS = AAS C. HL = HL D. SSS = SSS 23. If the three angles of a triangle are represented by (x + 30), (4x + 30), and (10x 30), the triangle must be 23. A. obtuse B. isosceles C. right D. scalene page 9

10 24. In the accompanying diagram of ABC, AB is extended through B to D. m CBD = 3x + 20, m A = x, and m ACB = x + 60, find x. If In the diagram below, four pairs of triangles are shown. Congruent corresponding parts are labeled in each pair. 25. A C B D Using only the information given in the diagrams, which pair of triangles can not be proven congruent? A. A B. B C. C D. D page 10

11 26. State the congruence relation for XYZ and PQR Which statement is not valid for proving that two triangles are congruent? What is the measure of the largest angle in the accompanying triangle? 28. page 11

12 29. Given: VY = WY VX = WZ Y is the midpoint of XZ 29. Prove: VXY = WYZ statement reason Y is the midpoint of XZ (1) XY = YZ (2) VY = WY (3) VX = WZ (4) VXY = WYZ (5) In the above proof, what is reason (2)? 30. Given: ABC, BED, AB = CB, and D is the midpoint of AC. Prove: AE = CE. 30. page 12

13 31. In the accompanying diagram, CA AB, ED DF, ED AB, CE = BF, AB = ED, and m CAB = m FDE = Which statement would not be used to prove ABC = DEF? 32. In the diagram of ABC and DEF below, AB = DE, A = D, and B = E. 32. Which method can be used to prove ABC = DEF? Determine the length of MN if ST is (3x + 2) units. page 13

14 34. Which statements could be used to prove that ABC and A B C are congruent? In the accompanying diagram, m A = 2x 30, m B = x, and m C = x Find the number of degrees in B. 35. page 14

15 Problem-Attic format version c EducAide Software Licensed for use by Terms of Use at 11/09/ Objective: 5. Objective: B BC = YZ and A = X SAS = SAS B G.CO.10 8x 3 2 G.SRT x C A A = L HL Objective: G.SRT ASA = ASA AAS Objective: SSS G.CO Objective: C reflexive property G.CO.10 B B Objective: 27. A Objective: not necessarily congruent G.CO.7 SSA = SSA definition of midpoint G.CO.10 [proof] SSS = SSS ASA 33. 6x + 4 Objective: G.SRT AB = A B, A = A, and C = C 18. AA

2. In the accompanying diagram, ABC and RST are right triangles with right angles at B and S, respectively; AB. = RS and AC = RT.

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