7.5 You Shouldn’t Make Assumptions Geometry 7.5 You Shouldn’t Make Assumptions

7.5 Angle-Side-Angle Congruence Theorem Objectives Explore the Angle-Side-Angle Congruence Theorem through constructions. Explore the Angle-Side-Angle Congruence Theorem on the coordinate plane. Prove the Angle-Side-Angle Congruence Theorem.

Two sets of corresponding sides are given congruent ∠𝐴≅∠𝐴 B Two sets of corresponding sides are given congruent ∠𝐴≅∠𝐴 Reflexive Property (Included Angle) ∆𝐴𝐵𝐸≅∆𝐴𝐶𝐷 SAS

One sets of corresponding sides are given congruent ∠𝐴𝐶𝐷≅∠𝐵𝐶𝐷 (Definition of Bisect) 𝐷𝐶 ≅ 𝐷𝐶 Reflexive Property ∆𝐴𝐶𝐷≅∆𝐵𝐶𝐷 SAS

Problem 1: Putting the Pieces Together Skip 1-3 Constructions Included Side The side between two consecutive angles of a triangle. Angle-Side-Angle Congruence Theorem (ASA) If two angles and the included side of one triangle are congruent to the corresponding two angles and the included side of another triangle, then the triangles are congruent.

Problem 1: Putting the Pieces Together Angle-Side-Angle Congruence Theorem (ASA) ∆𝐴𝐵𝐶≅∆𝐷𝐸𝐹 A C B D E F

Problem 2: How Did You Get There? Use the information below Collaborate #1 parts c & d (2 Minutes) ∆𝐴𝐵𝐶≅∆𝐷𝐸𝐹 ASA

Problem 3: And Finally the Proof… Collaborate (6 Minutes) May want to check out the proof from 7.4

A A ∆𝐴𝐷𝐵≅∆𝐴𝐷𝐶 ASA B D D C

Formative Assessment Skills Practice 7.5 Pg. 604-605 (13-20)