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Proving Triangles are Congruent ASA and AAS

Proving Triangles are Congruent ASA and AAS. Chapter 4.5 Objectives: To use the ASA and AAS Theorem to prove that triangles are congruent. ASA   Theorem.

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Proving Triangles are Congruent ASA and AAS

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  1. Proving Triangles are CongruentASA and AAS Chapter 4.5 Objectives: To use the ASA and AAS Theorem to prove that triangles are congruent

  2. ASA   Theorem • If two angles and the included side of one triangle, are congruent to the corresponding angles and side in a second triangle, then the triangles are congruent.

  3. Y B X A C Z ABC  XYZ — Why? ASA   Theorem

  4. Use ASA in Proofs Write a two-column proof.

  5. L is the midpoint of WE Step Reason Given Def of Midpt. Given W  E Alternate Int.  Thm. RLW  DLE Vertical  Thm. WRL  EDL ASA   Thm.

  6. Write a two-column proof.

  7. Step Reason Given CBD  ADB Alternate Int.  Thm. CDB  ABD Alternate Int.  Thm. Reflexive Property ABD  CDB ASA   Theorem.

  8. AAS   Theorem • If two angles and a non-included side of one triangle, are congruent to the corresponding angles and side in a second triangle, then the triangles are congruent.

  9. Y B X A C Z ABC  XYZ — Why? AAS   Theorem

  10. Write a two-column proof. JNM  KNL

  11. J K M L N N IMPORTANT HINT: When you are given overlapping triangles, draw them separately.

  12. J K M L N N Step Reason NKL  NJM Given Given JNM  KN L Reflexive Property JNM  KNL AAS   Thm.

  13. Homework Chapter 4-5 • Pg 238 1-4, 8, 9, 15, 27 These are all two-column proofs!!! Video B 7:40- Interactive Lab:Proofs and Congruent Triangles

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