1. 3.7 Angle-Side Theorems Objective:
After studying this lesson you will be able to apply theorems relating the angle measures and side lengths of triangles.

2. Given: Prove: Statement Reason
Theorem: if two sides of a triangle are congruent, the angles opposite the sides are congruent.
If , then C
Given:
Prove: A T
Statement
Reason 1. 2. 3. 4. 1. 2. 3. 4.

3. Given: Prove: Statement Reason
Theorem: if two angles of a triangle are congruent, then sides opposite the angles are congruent.
If , then B Y O
Given:
Prove:
Statement
Reason 1. 2. 3. 4. 1. 2. 3. 4.

4. Theorem:. If two sides of a triangle are not
Theorem: If two sides of a triangle are not congruent, then the angles opposite them are not congruent, and the larger angle is opposite the longest side. 80 60 40
Longest side
Theorem: If two angles of a triangle are not congruent, then the sides opposite them are not congruent, and the larger side is opposite the larger angle.

5. What are the restrictions on x?
Given: A
(6x-45)
(15+x) B C
What are the restrictions on x?

6. Prove: The bisector of the vertex angle of an isosceles triangle is also the median to the base.
Reason
Statement J M K 1. 2. 3. 4. 5. 6. 7. 8. 1. 2. 3. 4. 5. 6. 7. 8.

7. Given: Prove: Reason Statement T B A W X Y Z 3 4 1. 2. 3. 4. 5. 6. 7.8. 9. 1. 2. 3. 4. 5. 6. 7. 8. 9.

8. D
Given:
Prove: E F G H
Reason
Statement 1. 2. 3. 4. 1. 2. 3. 4.

9. Summary:
Where is the longest side located? The shortest?
If base angles are congruent what can we say about the triangle?
Homework: worksheet