1. 7.5 You Shouldn’t Make Assumptions
Geometry
7.5 You Shouldn’t Make Assumptions

2. 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.

3. 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

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

5. 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.

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

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

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

10. A A
∆𝐴𝐷𝐵≅∆𝐴𝐷𝐶
ASA B D D C

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