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Homework Lesson 4-1 ∆ ≅ ∆. Complete each congruence statement 1. ≅ ∠ 2. ≅ 3. ≅ ∠ 4. ≅ 5. ∆ ≅ ∆ 6. ≅ 7. ∆ ≅ ∆ 8. ∠ ≅ ∠ Mrs. Rivas Homework Mrs. Rivas Lesson 4-1 State whether the figures are congruent. Justify your answers. 9. ∆; ∆ Yes; corresponding sides and corresponding angles are ≅. Homework Mrs. Rivas Lesson 4-1 State whether the figures are congruent. Justify your answers. 10. ∆; ∆ No; the only corresponding part that is ≅ is . Homework Mrs. Rivas Lesson 4-1 State whether the figures are congruent. Justify your answers. 11. ⧠; ⧠ Yes; corresponding sides and corresponding angles are ≅. Homework Mrs. Rivas Lesson 4-1 State whether the figures are congruent. Justify your answers. 12.∆; ∆ Yes; corresponding sides and corresponding angles are ≅. Homework Mrs. Rivas Lessons 4-2 and 4-3 Can you prove the two triangles congruent? If so, write the congruence statement and name the postulate you would use. If not, write not possible and tell what other information you would need. 13. ∠ ≅ ∠ ≅ ∠ ≅ ∠ Homework Mrs. Rivas Lessons 4-2 and 4-3 Can you prove the two triangles congruent? If so, write the congruence statement and name the postulate you would use. If not, write not possible and tell what other information you would need. 14.. ≅ ≅ ∠ ≅ ∠ Homework Mrs. Rivas Lessons 4-2 and 4-3 Can you prove the two triangles congruent? If so, write the congruence statement and name the postulate you would use. If not, write not possible and tell what other information you would need. 15. Homework Mrs. Rivas Lessons 4-2 and 4-3 Can you prove the two triangles congruent? If so, write the congruence statement and name the postulate you would use. If not, write not possible and tell what other information you would need. 16. ≅ ≅ ≅ Homework Lessons 4-2 and 4-3 17. Given: ≅ , bisects . Prove: ∆ ∆ bisects means that ≅ . ≅ Given ≅ Reflective property of ≅ ∆ ≅ ∆ SSS ∠ ≅ ∠ Def. of ≅. ≅ Reflective property of ≅ ∆ ≅ ∆ by SAS. Mrs. Rivas Homework Mrs. Rivas Lessons 4-2 and 4-3 18. Given: ∠1 ≅ ∠2, ∠3 ≅ ∠4, ≅ , P is the midpoint of . Prove: ∆ ≅ ∆ It is given that ∠ ≅ ∠ and ∠ ≅ ∠. By the ⦨ Addition. Post., ∠ ≅ ∠. Since is the midpoint of , ≅ . It is given that ≅ , so ∆ ≅ ∆ by SAS. Homework Lesson 4-4 21. Given: ≅ , ∥ Prove: ∠ ≅ ∠ ∥ , so ∠ ≅ ∠. ≅ by the Reﬂexive Prop. of ≅. Since ≅ , ∆ ≅ ∆ by SAS, Then ∠ ≅ ∠ by CPCTC. Mrs. Rivas Homework Lesson 4-4 22. Given: ∠ ≅ ∠, ∠ ≅ ∠ Prove: ≅ ≅ Reﬂexive Prop. of ≅. Since ∠ ≅ ∠ and ∠ ≅ ∠ ∆ ≅ ∆ by AAS ≅ by CPCTC Mrs. Rivas Homework Mrs. Rivas Lesson 4-4 23. Given: ∠1 ≅ ∠2, ∠3 ≅ ∠4, is the midpoint of Prove: ∆ ≅ ∆ ∠ ≅ ∠,∠ ≅ ∠ Given ≅ Reflexive Property is the midpoint of , ≅ . ≅ Reflexive Property SSS ∆ ≅ ∆ AAS ∆ ≅ ∆ ≅ CPCTC ∠ ≅ ∠ CPCTC Homework Mrs. Rivas Lesson 4-4 24. Given: = , ∠1 ≅ ∠2, Prove: ∠ ≅ ∠ ∠ ≅ ∠,∠ ≅ ∠ Supplement of ≅ angles are ≅. ≅ Given ∠ ≅ ∠ Vertical ⦞ are ≅. ∆ ≅ ∆ ASA ∠ ≅ ∠ CPCTC Homework Mrs. Rivas Lesson 4-5 Find the value of each variable 25. + = = = Homework Mrs. Rivas Lesson 4-5 Find the value of each variable 26. + + = + = = Homework Mrs. Rivas Lesson 4-5 Find the value of each variable 27. + = = base angles are congruent = + = + = = Homework Mrs. Rivas Lesson 4-5 28. Given: ∠5 ≅ ∠6, ≅ Prove: ∆ is isosceles. ≅ Given ∠ ≅ ∠ Isosceles ∆ Theorem ∠ ≅ ∠ ≅ Supplement Theorem ∠ ≅ ∠ Given ∆ ≅ ∆ ≅ ASA CPCTC and ∆ is isosceles by Isosceles ∆ Theorem Homework Mrs. Rivas Lesson 4-5 29. Given: ≅ , ≅ Prove: ∆ is isosceles ≅ and ≅ Given ∠ ≅ ∠ Vertical ⦞ are ≅. ∆ ≅ ∆ SAS ∠ ≅ ∠ CPCTC ∠ ≅ ∠ Isosceles ∆ Theorem ∠ + ∠ = ∠ + ∠ Add. Prop. of ≅ so ∠ = ∠ by the ∠ Add. Post. and substitution. = by the Conv. of the Isosceles ∆ Theorem. ∆ is isosceles by Definition of Isosceles ∆. Homework Mrs. Rivas Lessons 4-6 and 4-7 Name a pair of overlapping congruent triangles in each diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL. 30. ∆ ≅ ∆; Homework Mrs. Rivas Lessons 4-6 and 4-7 Name a pair of overlapping congruent triangles in each diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL. 31. ∆ ≅ ∆; Homework Mrs. Rivas Lessons 4-6 and 4-7 Name a pair of overlapping congruent triangles in each diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL. 32. ∆ ≅ ∆; Homework Mrs. Rivas Lessons 4-6 and 4-7 Name a pair of overlapping congruent triangles in each diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL. 33. ∆ ≅ ∆; Homework Mrs. Rivas Lessons 4-6 and 4-7 34. Given: M is the midpoint of , ⊥ , ⊥ , ∠1 ≅ ∠2 Prove: ∆ ≅ ∆ ∠ ≅ ∠ Given ≅ by the Conv. of the Isosceles ∆ Theorem. ≅ by the Def. of Midpoint ≅ means that ∠ is a right angle and ∆ is a right ∆. ⊥ means that ∠ is a right ⦨ and ∆ is a right ∆ . ∆ ≅ ∆ by HL. Homework Mrs. Rivas 35. The longest leg of ∆, , measures 10 centimeters. measures 8 centimeters. You measure two of the legs of ∆ and find that ≅ and ≅ . Can you conclude that two triangles to be congruent by the HL Theorem? Explain why or why not. No; you only know that two sides (SS) are congruent, and you don’t know that there are right angles.