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Name __________________________________ ASA and AAS Triangle Congruency Homework Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. 1. 2. 3. Congruent? _____ Congruent? _____ Congruent? _____ If yes, state reason:______ If yes, state reason:______ If yes, state reason:______ State the third congruence that is needed to prove that ∆DEF ≅ ∆ABC using the given postulate or theorem. 4. GIVEN: DE ≅ AB , ∠D ≅ ∠A. ______ ≅ ______ Use the AAS Congruence Theorem. 5. GIVEN: FE ≅ CB , ∠F ≅ ∠C. ______ ≅ ______ Use the ASA Congruence Postulate. 6. GIVEN: DF ≅ AC , ∠F ≅ ∠C. ______ ≅ ______ Use the SAS Congruence Theorem. State the third congruence that is needed to prove that ∆ABC ≅ ∆XYZ >.using the given postulate or theorem. 7. GIVEN: ∠C ≅ ∠Z, AC ≅ XZ ______ ≅ ______ Use the AAS Congruence Theorem. 8. GIVEN: ∠B ≅ ∠Y, AB ≅ XY , ______ ≅ ______ Use the ASA Congruence Postulate. 9. GIVEN: BC ≅ YZ . ∠B ≅ ∠Y. ______ ≅ ______ Use the SAS Congruence Theorem. State the third congruence that is needed to prove that ∆DEF= ∆MNO using the given postulate or theorem. 10. GIVEN: DE ≅ MN ,∠M ≅ ∠D, ______ ≅ ______ Use the SAS Congruence Postulate. 11.GIVEN: FE ≅ ON ,∠F ≅ ∠O, ______ ≅ ______ Use the AAS Congruence Theorem. 12.GIVEN: DF ≅ MO ,∠F ≅ ∠O, ______ ≅ ______ Use the ASA Congruence Postulate. Draw and label triangles to illustrate the given information. Then tell whether you can use the given information to determine whether ∆JKL ≅ ∆RST. If the triangles are congruent, give a reason. 13. ∠J ≅ ∠R, ∠K ≅ ∠S, ∠L ≅ ∠T Congruent?_____ If yes,reason:_____ 14. ∠K ≅ ∠S, ∠L ≅ ∠M , KL ≅ ST Congruent?_____ If yes,reason:_____ 15. JM ≅XZ , ∠M ≅ ∠Z, ∠R ≅ ∠Y Congruent?_____ If yes,reason:_____ JM ≅ XZ , JR ≅ XY , ∠J ≅ ∠X Congruent?_____ If yes,reason:_____ 17. ∠J ≅ ∠X, ∠M ≅ ∠Z, ∠R ≅ ∠Y Congruent?_____ If yes,reason:_____ 16. 18. Multiple Choice Which postulate or theorem can you use to prove that ∆ABC ≅ ∆DEF? A. AAS B. SA C. SAS D. Not enough information Explain how you can prove that the indicated triangles are congruent using the given postulate or theorem. (State the appropriate side or angle.) 19. ∆ABE ≅ ∆CDE by SAS Sides:_____ 20. ∆ABE ≅ ∆CDE by ASA Angles:_____ Sides:_____ Angles:_____ 21. ∆ABE ≅ ∆CDE by AAS Angles:_____ Angles:_____ Sides:_____ Angles:_____ Sides:_____ GIVEN:VW ≅ XY ,WX ≅ YV PROVE: ∆WXV ≅ ∆AYVX Statements 1. VW ≅ XY Reasons 1. 2. WX ≅ YV 2. 3. VX ≅ VX 3. 4. ∆VWX ≅ ∆XYV 4. 5. ∆WXV ≅ ∆YVX 5. 19. Proof Write a proof. GIVEN: BE ≅ BC , ∠A ≅ ∠D PROVE: ∆ABE ≅ ∆DBC 17. Proof Complete the proof. GIVEN: WU || YV, XU || ZV, WX ≅ YZ PROVE: ∆WXU ≅ ∆YZV Statements 1. WU ||YV 2. ∠UWX ≅ ∠VYZ 3. XU || ZV 4. ∠UWX ≅ ∠VZY Reasons 1. 2. 3. 4. 5. WX || YZ 5. 6. ∆UWX ≅ ∆YZV 6.