Download 7.5 ASA - Van Buren Public Schools

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.
A
A
E
B
D
C
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)
A
∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹
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 (7 Minutes)
 May want to check out the proof from 7.4
Finish This Proof (3 Minutes)
A
A
∆𝐴𝐷𝐵 ≅ ∆𝐴𝐷𝐶
ASA
B
D
D
C
Formative Assessment
 Skills Practice 7.5
 Pg. 604-605 (13-20)