4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence.

Angle-Side-Angle Congruence Postulate (ASA) If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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Use ASA to Prove Triangles Congruent Statements Reasons 1. Given 1. L is the midpoint of WE. ____ 2. Midpoint Theorem 2. 3. Given 3. 4. Alternate Interior Angles 4. W  E 5. Vertical Angles Theorem 5. WLR  ELD 6. ASA 6. ΔWRL  ΔEDL

Fill in the blank in the following paragraph proof. A. SSS B. SAS C. ASA D. AAS

Side-Angle-Side Congruence Postulate (SAA) If two angles and a side opposite one of them in one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent.

Try It If possible, what is the congruence statement for this pair of triangles? If the triangles are not congruent, say so. Needs more information M N O A B C

Try It If possible, what is the congruence statement for this pair of triangles? If the triangles are not congruent, say so. D E F 20° 130° P Q 20° 130° R

Write a paragraph proof. Proof: NKL  NJM, KL  MN, and N  N by the Reflexive property. Therefore, ΔJNM  ΔKNL by AAS. By CPCTC, LN  MN. __ ___

Complete the following flow proof. A. SSS B. SAS C. ASA D. AAS

The curtain decorating the window forms 2 triangles at the top The curtain decorating the window forms 2 triangles at the top. B is the midpoint of AC. AE = 13 inches and CD = 13 inches. BE and BD each use the same amount of material, 17 inches. Which method would you use to prove ΔABE  ΔCBD? A. SSS B. SAS C. ASA D. AAS

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What are the four short cuts to prove triangles congruent? Side-Side-Side (SSS) Side-Angle-Side (SAS) Angle-Side-Angle (ASA) Side-Angle-Angle (SAA)

4-5 Assignment Page 278, 1, 4, 9, 10 Write as a two column proof. Write out Given and Prove. Draw the figure.