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Congruent Triangles Name: 1. Date: 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 ? 4. A. SAS = SAS A. HL = HL B. ASA = ASA B. SSS = SSS C. HL = HL C. ASA = ASA D. SAS = SAS D. AAS = AAS 2. In the accompanying diagram, ^ABC and ^RST are right triangles with right angles at B and S, respectively; AB = RS and AC = RT. 5. Which statement can be used to justify that ^ABC = ^RST ? A. SAS = SAS B. C. HL = HL D. SAA = SAA In the accompanying diagram, PR = SQ, PR ? RQ, and SQ ? RQ. Which statement can be used to prove that ^PQR = ^SRQ ? A. AAS = AAS B. SAS = SAS C. HL = HL D. SSS = SSS ASA = ASA 6. 3. In the accompanying diagram of quadrilateral ABCD, diagonal AC bisects OBAD and OBCD. Which statement can be used to prove that ^ABC = ^ADC ? Two triangles are congruent if 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 ? A. corresponding angles are congruent A. HL B. B. corresponding sides and corresponding angles are congruent C. AAS D. ASA C. the angles in each triangle have a sum of 180 D. corresponding sides are proportional page 1 SAS 7. 10. In the accompanying diagram, RL ? LP, LR ? RT, and M is the midpoint of TP. Which method could be used to prove ^ TMR = ^PML ? A. SAS = SAS B. AAS = AAS C. HL = HL Which statement can be used to prove ^STY = ^ DTU? D. SSS = SSS 8. 11. ! ! ! In the accompanying diagram, ACE, BCD, AB, ! and DE, OA = OE, and C is the midpoint of AE. Which theorem justi es ^ABC = ^EDC ? A. SSS = SSS B. SAS = SAS C. ASA = ASA In the accompanying diagram, point T is the midpoint of SD and YU; SY and UD are drawn. A. SSS = SSS B. C. ASA = ASA D. HL = HL SAS = SAS In the accompanying diagram, E is the midpoint of AB and CD. D. SSA = SSA Triangle AEC can be proved congruent to triangle BED by 9. In the accompanying diagram of isosceles triangle ABC, OACB is the vertex angle, CM ? AB, and M is the midpoint of AB. Which statement can not be used to justify ^ACM = ^BCM ? A. HL = HL B. AAS = AAS C. SSS = SSS 12. A. AAS = AAS B. C. SAS = SAS D. SSS = SSS ASA = ASA In the accompanying diagram, AB and CD intersect at E, E is the midpoint of AB, and OA = OB. Which statement can be used to prove ^ADE = ^BCE D. AAA = AAA page 2 A. ASA = ASA B. C. SSS = SSS D. SAS = SAS HL = HL Congruent Triangles 13. 15. In the accompanying diagram, HK bisects IL and OH = OK. In the diagram of ^ABC and ^DEF below, AB = DE, OA = OD, and OB = OE. What is the most direct method of proof that could be used to prove ^HIJ = ^KLJ? A. HL = HL B. C. AAS = AAS D. ASA = ASA Which method can be used to prove ^ABC = ^DEF? SAS = SAS A. 16. 14. In the accompanying diagram of triangles BAT and FLU, O B = OF and BA = FL. SSS B. SAS C. ASA D. HL If ^JKL = ^MNO, which statement is always true? A. OKLJ = ONMO B. C. JL = MO D. JK = ON OKJL = O MON Which statement is needed to prove ^BAT = ^ FLU? 17. A. OA = OL B. C. OA = OU D. BA k FL In the diagram below, ^ABC = ^XYZ. AT = LU Which statement must be true? page 3 A. OC = O Y B. C. AC = YZ D. CB = XZ OA = OX Congruent Triangles 18. As shown in the diagram below, AC bisects OBAD and OB = OD. 20. In the diagram below of ^DAE and ^BCE, AB and CD intersect at E, such that AE = CE and OBCE = ODAE. Which method could be used to prove ^ABC = ^ADC? A. SSS B. AAA C. SAS Triangle DAE can be proved congruent to triangle BCE by D. AAS A. 19. 21. The diagram below shows a pair of congruent triangles, with OADB = OCDB and OABD = O CBD. ASA B. SAS C. SSS D. HL In the diagram below, four pairs of triangles are shown. Congruent corresponding parts are labeled in each pair. A C B D Which statement must be true? A. OADB + OCBD B. OABC + OADC C. AB = CD D. AD = CD Using only the information given in the diagrams, which pair of triangles can not be proven congruent? A. page 4 A B. B C. C D. D Congruent Triangles 22. In the accompanying diagram of isosceles triangle ABC, AB = BC, mOBAC = x, and mOABC = x + 30. 25. What is the value of x ? A. 80 B. C. 50 D. 30 The accompanying diagram shows the roof of a house that is in the shape of an isosceles triangle. The vertex angle formed at the peak of the roof is 84 . 75 What is the measure of x? 23. A. In the diagram below of ^ABC, AB = AC, mOA = 3x, and mOB = x + 20. 138 B. 96 C. 84 D. 48 26. In the accompanying diagram of ^ABC, CB = CA, is extended to D, and mOB = 42. Find mOCAD. 27. In the accompanying diagram of isosceles triangle SUM, SM = UM and OMUD is an exterior angle formed by extending SU to D. If mOMUD = 124, nd mOM. What is the value of x? A. 24. 10 B. 28 C. 32 D. 40 In the accompanying diagram, isosceles ^ABC = isosceles ^DEF, mOC = 5x, and mO D = 2x + 18. Find mOB and mOBAG. page 5 Congruent Triangles 28. Given that ABCD is a parallelogram, a student wrote the proof below to show that a pair of its opposite angles are congruent. Statement Reason 1. ABCD is a parallelogram. 1. Given 3. AC = CA 3. Re exive Postulate of Congruency 2. BC = AD AB = DC 4. ^ABC = ^CDA 5. OB = OD 2. Opposite sides of a parallelogram are congruent. 4. Side-Side-Side 5. What is the reason justifying that OB = OD? A. Opposite angles in a quadrilateral are congruent. B. Parallel lines have congruent corresponding angles. C. Corresponding parts of congruent triangles are congruent. D. Alternate interior angles in congruent triangles are congruent. page 6 Congruent Triangles