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Name: ___________________________________ Geometry A Chapter 4 Review Section 4-2 Section 4-1 In Problems 1 and 2, quadrilateral WASH quadrilateral NOTE. 1. List (all 8) corresponding parts. 1. In VGB , which sides include B ? 2. In STN , which angle is included between NS and TN ? 2. m O m T 90 and m H 36 . Find m N . 3. Which triangles can you prove congruent? Tell whether you would use the SSS or SAS Postulate. Y A 3. Write a statement of triangle congruence. P X P Z F B D H 4. What other information do you need to prove DWO DWG ? R D 4. Write a statement of triangle congruence. B A 1 2 W O C G D 5. Explain your reasoning in Problem 4 above. 5. Can you prove SED BUT from the information given? Explain. U D T E S B A 3. Additional Examples 1. Suppose that F is congruent to C and I is NOT congruent to C . Name the triangles that are congruent by the ASA Postulate. D O C T G A 2 D F C Given: B D , AB || CD Prove: ABC CDA I N A Y 2. X B 1 P B Given: A B , AP BP Prove: APX BPY P O 4. Q S 1 2 R Given: S Q , RP bisects SRQ Prove: SRP QRP CLOSURE Explain why the letters of ASA and AAS are written in a different order. Section 4-3 1. Which side is included between R and F in FTR ? Section 4-4 1. What does “CPCTC” stand for? Use the diagram for Problems 2 and 3. A 2. Which angles in STU include US ? C B M Tell whether you can prove the triangles congruent by ASA or AAS. If you can, state a triangle congruence and the postulate or theorem you used. If not, write NOT POSSIBLE. 3. G 2. Tell how you would show ABM ACM . P H I Q R 3. Tell what other parts are congruent by CPCTC. L P 4. Use the diagram for Problems 4 and 5. Y S A R U T Q A 4. Tell how you would show RUQ TUS . 5. B X C 5. Tell what other parts are congruent by CPCTC. Section 4-5 Use the diagram for Problems 1-3. Section 4-6 For Problems 1 and 2, tell whether the HL Theorem can be used to prove the triangles congruent. If so, explain. If no, write NOT POSSIBLE. 1. A A B B C M C 1. If m BAC 38 , find m C . R D 2. If m BAM m CAM 23 , find m BMA. Q 2. E T W 3. If m B 3 x and m BAC 2 x 20 , find x . For Problems 3 and 4, what additional information do you need to prove the triangles congruent by the HL Theorem? 3. LMX LOX 4. Find the values of x and y. M L X 60 18 60 O N y 60 x 5. ABCDEF is a regular hexagon. Find m BAC . A 4. AMD CNB B N A C F D E D M C B Section 4-7 1. Identify any common sides and angles in AXY and BYX . A REVIEW PROBLEMS 1. Given: AB BC ; DC BC ; 1 2 Prove: AC DB A D X E Y 2 1 B C B For Problems 2 and 3, name a pair of congruent overlapping triangles. State the theorem or postulate that proves them congruent. 2. K M T S R M P 2. 3 H G R 4 3. J J I A 4. Given: PK and JM bisect each other at R. Prove: PJ MK B X D 1 K 2 Given: AC BD , AD BC Prove: XD XC I 3. Given: KRM PRO , KR PR Prove: RM RO R K 4. 2 M E A 3 B 1 4 O D 5 6 C Given: 3 6 ; 3 is comp. 4 ; 6 is comp. 5 Prove: EBC is isosceles C