Download Worksheet C: SAS and SSA investigations

Name: Thomas Haas
Lesson Title: Congruent Triangles Challenge
Activity Title: Congruence shortcuts
Contact Info: [email protected]
Unit #:
3
Lesson #:
2
Date:24-Jul-13
Activity #:
1
Worksheet:
c
Worksheet Title: Testing SAS and SSA
Investigation 3: Is SAS a way to determine congruent triangles?
The question that will be answered: If two sides and the included angle of one triangle are
congruent to two sides and the included angle of another, must the triangles be congruent?
An angle that is between two sides of a triangle is called an included angle.
Each member of the group will complete step 1 on their own.
Step 1: Construct a triangle from the three parts shown above. Be sure you match up the endpoints
as labeled with the same letter.
Step 2: Compare your triangle with the triangles made by others in your group. Make sure that your
comparison is valid. Is it possible to construct different triangles with two pairs of sides congruent
and the included angles congruent or will all the triangles always be congruent?
Step 3: Talk with your group and develop a conjecture about the SAS case.
1
Investigation 4: Is SSA a way to determine congruent triangles?
The question that will be answered: If two sides and a non-included angle of one triangle are
congruent to the corresponding two sides and non-included angle of another triangle, must the two
triangles be congruent?
Each member of the group will complete step 1 on their own.
Step 1: Construct a triangle from the three parts shown above. Be sure you match up the endpoints
as labeled with the same letter.
Step 3: Compare your triangle with the triangles made by others in your group. Is it possible to
construct different triangles with two pairs of sides congruent and a corresponding pair of nonincluded angles congruent, or will all the triangles that can be constructed always be congruent?
Step 4: Talk with your group and develop a conjecture about the SSA case.
2