Download 7.4 SAS - Van Buren Public Schools

Geometry
7.4 SIDE-ANGLE-SIDE
7.4 Side-Angle-Side
Congruence Theorem
 Objectives
 Explore the Side-Angle-Side Congruence Theorem using
constructions.
 Explore the Side-Angle-Side Congruence Theorem on the
coordinate plane.
 Prove the Side-Angle-Side Congruence Theorem.
Problem 1
Using Constructions to Support Side-Angle-Side
 Included Angle
 The angle formed by two adjacent sides of a triangle.
 Side-Angle-Side Congruence Theorem
 If two sides and the included angle of one triangle are
congruent to the corresponding sides and the included angle of
the second triangle, then the triangles are congruent. (SAS)
Problem 1
Using Constructions to Support Side-Angle-Side
Side-Angle-Side Congruence Theorem (SAS)
A
∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹
C
B
D
E
F
Problem 2
Using Rotations to Support Side-Angle-Side
 Collaborate 1-2 (3 Minutes)
𝑑=
𝑥2 − 𝑥1
2
+ 𝑦2 − 𝑦1
2
Problem 2
Using Rotations to Support Side-Angle-Side
 Together #3
Problem 2
Using Rotations to Support Side-Angle-Side
 Together 4-5
𝑑=
𝑥2 − 𝑥1
2
+ 𝑦2 − 𝑦1
2
Problem 2
Using Rotations to Support Side-Angle-Side
 Together #6
 The corresponding angles are congruent
 Together #7
Which is the included angle between
the selected sides?
• 𝑅𝑁 𝑎𝑛𝑑 𝑃𝑁
• 𝐴𝑀 𝑎𝑛𝑑 𝑄𝑀
∠𝑁
∠𝑀
Problem 2
Using Rotations to Support Side-Angle-Side
 Together #6
 The corresponding angles are congruent
 Together #7
Which is the included angle between
the selected sides?
• 𝑅𝑁 𝑎𝑛𝑑 𝑃𝑁
• 𝐴𝑀 𝑎𝑛𝑑 𝑄𝑀
∠𝑁
∠𝑀
• 𝑅𝑃 𝑎𝑛𝑑 𝑁𝑃
• 𝑄𝐴 𝑎𝑛𝑑 𝑀𝐴
∠𝑃
∠𝐴
Problem 3: And Finally the Proof…
 Collaborate (6 Minutes)
 May want to check out the proof from 7.3
Problem 4
Writing Congruence Statements
Together #1
What would be the information
needed to prove by SAS?
𝐴𝐵 ≅ 𝐷𝐶
∠𝐴𝐵𝐶 ≅ ∠𝐷𝐶𝐵
𝐵𝐶 ≅ 𝐶𝐵
Problem 4
Writing Congruence Statements
 Collaborate 2-3 (4 Minutes)
SSS
SAS
Problem 4
Writing Congruence Statements
The triangles are not congruent.
The angle is not an included angle.
There is no SSA theorem.
Problem 4
Writing Congruence Statements
Use the straws to make an example that SSA does not work
Formative Assessment
 Skills Practice 7.4
 Pg. 592-595 (13-28)