3.7 Angle-Side Theorems

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.

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.

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

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.

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

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

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

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

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

3.7 Angle-Side Theorems