# Geometry CP - Ch. 4 Review

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1 Geometry CP - Ch. 4 Review 1. If, which of the following can you NOT conclude as being true? A. B. C. D. 2. A. B. C. D. 3. Given and, find the length of QS and TV. A. 7 B. 25 C. 8 D The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to scale. g 21 b 13 d 12 f 5 e 69 c A. 5 B. 21 C. 13 D Justify the last two steps of the proof. Given: and Prove:

2 R S T U Proof: Given Given A. Reflexive Property of ; SAS C. Reflexive Property of ; SSS B. Symmetric Property of ; SSS D. Symmetric Property of ; SAS 6. What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate? A ( ( B C D A. C. B. D. 7. Which triangles are congruent by ASA?

3 ( F T )) V ( A (( B G ) U H C A. C. B. D. none 8. Which pair of triangles is congruent by ASA? A. C. B. D. 9. If and, which additional statement does NOT allow you to conclude that?

4 A. C. B. D. 10. Can you use the SAS Postulate, the AAS Theorem, or both to prove the triangles congruent? ) ) A. SAS only C. AAS only B. either SAS or AAS D. neither 11. What is the value of x? xº Drawing not to scale A. 156 B. 146 C. 73 D Supply the missing reasons to complete the proof. Given: and Prove:

5 S U T R V A. ASA; Substitution C. ASA; Corresp. parts of B. AAS; Corresp. parts of D. SAS; Corresp. parts of 13. What is the value of x? xº 74 Drawing not to scale A. 32 B. 106 C. 53 D Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence statement?

6 A B C D A. Yes;. B. Yes;. C. Yes;. D. No, the triangles cannot be proven congruent. 15. What additional information will allow you to prove the triangles congruent by the HL Theorem? A B C D E A. C. B. D. 16. What common side do A B C D E F G H

7 A. C. B. D. 17. What common angle do C D E F G A. C. B. D. 18. Find the value of x. The diagram is not to scale. S R (3x 50) (7x) T U 19. The legs of an isosceles triangle have lengths and. The base has length. What is the length of the base? 20. Two sides of an equilateral triangle have lengths and. Which expression could be the length of the third side: or?

8 21. Find the value of x. The diagram is not to scale. Given:, S R T U

9 Geometry CP - Ch. 4 Review Answer Section 1. ANS: A PTS: 1 DIF: L3 REF: 4-1 Congruent Figures OBJ: To recognize congruent figures and their corresponding parts NAT: CC G.SRT.5 G.2.e G.3.e TOP: 4-1 Problem 1 Finding Congruent Parts KEY: congruent polygons corresponding parts word problem 2. ANS: D PTS: 1 DIF: L2 REF: 4-1 Congruent Figures OBJ: To recognize congruent figures and their corresponding parts NAT: CC G.SRT.5 G.2.e G.3.e TOP: 4-1 Problem 1 Finding Congruent Parts KEY: congruent polygons corresponding parts 3. ANS: A PTS: 1 DIF: L4 REF: 4-1 Congruent Figures OBJ: To recognize congruent figures and their corresponding parts NAT: CC G.SRT.5 G.2.e G.3.e TOP: 4-1 Problem 2 Using Congruent Parts KEY: congruent polygons corresponding parts 4. ANS: A PTS: 1 DIF: L3 REF: 4-1 Congruent Figures OBJ: To recognize congruent figures and their corresponding parts NAT: CC G.SRT.5 G.2.e G.3.e TOP: 4-1 Problem 2 Using Congruent Parts KEY: congruent polygons corresponding parts 5. ANS: C PTS: 1 DIF: L3 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: To prove two triangles congruent using the SSS and SAS Postulates NAT: CC G.SRT.5 G.2.e G.3.e G.5.e TOP: 4-2 Problem 1 Using SSS KEY: SSS reflexive property proof 6. ANS: D PTS: 1 DIF: L4 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: To prove two triangles congruent using the SSS and SAS Postulates NAT: CC G.SRT.5 G.2.e G.3.e G.5.e TOP: 4-2 Problem 2 Using SAS KEY: SAS reasoning 7. ANS: A PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: To prove two triangles congruent using the ASA Postulate and the AAS theorem NAT: CC G.SRT.5 G.2.e G.3.e G.5.e TOP: 4-3 Problem 1 Using ASA KEY: ASA 8. ANS: D PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: To prove two triangles congruent using the ASA Postulate and the AAS theorem NAT: CC G.SRT.5 G.2.e G.3.e G.5.e TOP: 4-3 Problem 1 Using ASA KEY: ASA 9. ANS: B PTS: 1 DIF: L3 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: To prove two triangles congruent using the ASA Postulate and the AAS theorem NAT: CC G.SRT.5 G.2.e G.3.e G.5.e TOP: 4-3 Problem 4 Determining Whether Triangles Are Congruent KEY: ASA AAS 10. ANS: C PTS: 1 DIF: L3 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: To prove two triangles congruent using the ASA Postulate and the AAS theorem NAT: CC G.SRT.5 G.2.e G.3.e G.5.e TOP: 4-3 Problem 4 Determining Whether Triangles Are Congruent KEY: ASA AAS reasoning

10 11. ANS: C PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles NAT: CC G.CO.10 CC G.CO.13 CC G.SRT.5 G.1.c G.2.e G.3.e TOP: 4-5 Problem 2 Using Algebra KEY: isosceles triangle Converse of Isosceles Triangle Theorem Triangle Angle-Sum Theorem 12. ANS: C PTS: 1 DIF: L3 REF: 4-4 Using Corresponding Parts of Congruent Triangles OBJ: To use triangle congruence and corresponding parts of congruent triangles to prove that parts of two triangles are congruent NAT: CC G.CO.12 CC G.SRT.5 G.2.e G.3.e TOP: 4-4 Problem 1 Proving Parts of Triangles Congruent KEY: ASA corresponding parts proof two-column proof 13. ANS: A PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles NAT: CC G.CO.10 CC G.CO.13 CC G.SRT.5 G.1.c G.2.e G.3.e TOP: 4-5 Problem 2 Using Algebra KEY: isosceles triangle Isosceles Triangle Theorem Triangle Angle-Sum Theorem word problem 14. ANS: B PTS: 1 DIF: L2 REF: 4-6 Congruence in Right Triangles OBJ: To prove right triangles congruent using the hypotenuse-leg theorem NAT: CC G.SRT.5 G.2.e G.3.e G.5.e TOP: 4-6 Problem 1 Using the HL Theorem KEY: hypotenuse HL Theorem right triangle reasoning 15. ANS: C PTS: 1 DIF: L3 REF: 4-6 Congruence in Right Triangles OBJ: To prove right triangles congruent using the hypotenuse-leg theorem NAT: CC G.SRT.5 G.2.e G.3.e G.5.e TOP: 4-6 Problem 2 Writing a Proof Using the HL Theorem KEY: hypotenuse HL Theorem right triangle reasoning 16. ANS: D PTS: 1 DIF: L3 REF: 4-7 Congruence in Overlapping Triangles OBJ: To identify congruent overlapping triangles NAT: CC G.SRT.5 G.2.e G.3.e G.5.e TOP: 4-7 Problem 1 Identifying Common Parts KEY: overlapping triangle congruent parts 17. ANS: C PTS: 1 DIF: L2 REF: 4-7 Congruence in Overlapping Triangles OBJ: To identify congruent overlapping triangles NAT: CC G.SRT.5 G.2.e G.3.e G.5.e TOP: 4-7 Problem 1 Identifying Common Parts KEY: overlapping triangle congruent parts 18. ANS: PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles NAT: CC G.CO.10 CC G.CO.13 CC G.SRT.5 G.1.c G.2.e G.3.e TOP: 4-5 Problem 3 Finding Angle Measures KEY: Isosceles Triangle Theorem isosceles triangle 19. ANS: 11 PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles NAT: CC G.CO.10 CC G.CO.13 CC G.SRT.5 G.1.c G.2.e G.3.e TOP: 4-5 Problem 2 Using Algebra KEY: isosceles triangle Isosceles Triangle Theorem word problem problem solving 20. ANS: 18 x only

11 PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles NAT: CC G.CO.10 CC G.CO.13 CC G.SRT.5 G.1.c G.2.e G.3.e TOP: 4-5 Problem 2 Using Algebra 21. ANS: 14 KEY: equilateral triangle word problem problem solving PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles NAT: CC G.CO.10 CC G.CO.13 CC G.SRT.5 G.1.c G.2.e G.3.e TOP: 4-5 Problem 2 Using Algebra KEY: Isosceles Triangle Theorem isosceles triangle problem solving Triangle Angle-Sum Theorem

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