Proving Triangles are Congruent ASA and AAS

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Proving Triangles Congruent

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Proving Triangles Congruent

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Presentation transcript:

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 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.

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

Use ASA in Proofs Write a two-column proof.

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

Write a two-column proof.

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

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.

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

Write a two-column proof. JNM  KNL

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

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

Interactive Lab: Proofs and Congruent Triangles 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