Use the ASA Postulate to test for congruence. Use the AAS Theorem to test for congruence. Splash Screen

G.CO.10 Prove theorems about triangles. Content Standards G.CO.10 Prove theorems about triangles. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. 5 Use appropriate tools strategically. CCSS

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Write a two-column proof. Use ASA to Prove Triangles Congruent Write a two-column proof. Example 1

4. Alternate Interior Angles 4. W  E Use ASA to Prove Triangles Congruent Proof: 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 Example 1

Fill in the blank in the following paragraph proof. A. SSS B. SAS C. ASA D. AAS Example 1

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Write a paragraph proof. Use AAS to Prove Triangles Congruent 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. __ ___ Example 2

Complete the following flow proof. A. SSS B. SAS C. ASA D. AAS Example 2

Apply Triangle Congruence MANUFACTURING Barbara designs a paper template for a certain envelope. She designs the top and bottom flaps to be isosceles triangles that have congruent bases and base angles. If EV = 8 cm and the height of the isosceles triangle is 3 cm, find PO. Example 3

NV  EN by definition of isosceles triangle Apply Triangle Congruence In order to determine the length of PO, we must first prove that the two triangles are congruent. ____ ΔENV  ΔPOL by ASA. NV  EN by definition of isosceles triangle ____ EN  PO by CPCTC. ____ NV  PO by the Transitive Property of Congruence. ____ Since the height is 3 centimeters, we can use the Pythagorean theorem to calculate PO. The altitude of the triangle connects to the midpoint of the base, so each half is 4. Therefore, the measure of PO is 5 centimeters. Answer: PO = 5 cm Example 3

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 Example 3

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Homework Page 279 (6,7,9,10,11) Concept