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Quiz 5.1-5.4 Review Geometry Name:_________________________________ Decide whether the given angles or sides are corresponding angles, corresponding sides, or neither. 1. ∠C and ∠S 2. ̅̅̅̅ 𝑆𝑅 and ̅̅̅̅ 𝐷𝐸 ̅̅̅̅ 3. ̅̅̅̅ 𝐶𝐸 and 𝑅𝑇 4. ∠D and ∠S ̅̅̅̅ 5. ̅̅̅̅ 𝐷𝐸 and 𝑆𝑇 6. ∠E and ∠T For #7-9, the triangles at the right are congruent. 7. Identify all corresponding congruent angles. 8. Identify all corresponding congruent sides. 9. Write a congruence statement. ∆ _____ ≅ ∆ _______ In the diagram, ∆ABC ≅ ∆VTU. Find the indicated measure. 10. m ∠B = 11. AB = 12. m ∠T = 13. m ∠V = In the diagram, ∆FGH ≅ ∆LMN. 14. MN = 15. GF = 16. m ∠N = 17. m ∠F = In the diagram at the right, ∆ABC ≅ ∆PQR. 18. Mark every angle of the triangles to show the corresponding congruent angles. 19. Mark every side of the triangles to show the corresponding congruent sides. Determine whether the triangles are congruent. If so, write a congruence statement. 20. 21. Are the triangles congruent? Yes/no (circle one) Are the triangles congruent? Yes/no (circle one) If so, ∆YWX ≅ ∆_______ If so, ∆BCD ≅ ∆__________ Does the diagram give enough information to use the SSS congruence Postulate? 22. 23. yes/no (circle one) 24. yes/no (circle one) yes/no (circle one) Use the diagram shown to name the angle included between the two sides. ̅̅̅̅ and 𝐵𝐷 ̅̅̅̅ 25. 𝐴𝐵 ̅̅̅̅ and 𝐵𝐶 ̅̅̅̅ 26. 𝐶𝐷 ̅̅̅̅ and 𝐶𝐵 ̅̅̅̅ 27. 𝐴𝐶 ̅̅̅̅ and 𝐴𝐷 ̅̅̅̅ 28. 𝐵𝐴 Decide whether there is enough information given to use the SAS congruence postulate. 29. 30. 31. yes/no (circle one) yes/no (circle one) yes/no (circle one) Based on the diagram, can you use the ASA or the AAS congruence postulate to show that the two triangles are congruent? 32. ASA or AAS? (circle one) 33. ASA or AAS? (circle one) 34. ASA or AAS? (circle one) Name the postulate which could be used to show the triangles are congruent. Don’t forget to mark "free" sides and angles! Fill in the congruence statement where indicated. Choices are: SSS, SAS, ASA, AAS, HL or none. 35. 36. 37. 38. Postulate __________ Postulate __________ Postulate __________ Postulate __________ MON ________ PQR ________ LJK ________ FED ________ 39. 40. 41. 42. Postulate __________ Postulate __________ Postulate __________ Postulate __________ STR ________ ZYX ________ ADC ________ ADC ________ 43. 44. 45. 46. U Postulate __________ Postulate __________ Postulate __________ Postulate __________ ABC ________ PQR ________ KJM ________ UHS ________ 47. 48. 49. Postulate __________ Postulate __________ Postulate __________ Fill in the blanks for the following proofs. ̅̅̅̅ ≅ 𝐶𝐷 ̅̅̅̅ 𝐵𝐶 ̅̅̅̅ ≅ 𝐴𝐷 ̅̅̅̅ 50. Given: 𝐴𝐵 Prove: ABC CDA Statements 1. Reasons _______ 1. Given 2. 2. Given 3. ̅̅̅̅ AC ≅ ̅̅̅̅ CA 3. 4. ∆ABC ≅ ∆CDA 4. 51. Given: B is the midpoint of AE B is the midpoint of CD Prove: ABD EBC Statements Reasons 1. B is the midpoint of AE 1.___________________________ ̅̅̅̅ 2. B is the midpoint of 𝐶𝐷 2.____________________________ 3._______________________ 3. Definition of midpoint 4._______________________ 4. Definition of midpoint 5. ∠ABD ≅ ∠EBC 5. ___________________________ 6. _______________________ 6. SAS 52. Given: AB // CD , AB CD Prove: ABC DCB Statements Reasons 1.̅̅̅̅̅ 𝐴𝐵 // ̅̅̅̅ 𝐶𝐷 1.___________________________ 2. ______________________ 2. Given 3._______________________ 3. Reflexive 4. ∠ABC ≅ ∠DCB 4. ___________________________ 5. ∆ABD ≅ ∆DCB 5. ___________________________ 53. Given: ∠ACB and ∠ACD are right angles, ̅̅̅̅ 𝐴𝐵 ≅ ̅̅̅̅ 𝐴𝐷 Prove: ∆ABC ≅ ∆ADC Statements Reasons 1.∠ACB and ∠ACD are right angles 1. 2. _______________________ 2. Given 3. _______________________ 3. Definition of Right Triangles 4. ̅̅̅̅ 𝐴𝐶 ≅ ̅̅̅̅ 𝐴𝐶 4. 5. ∆ABC ≅ ∆ADC 5. ______________________________