1 / 9

# 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:.

Télécharger la présentation

## 3.7 Angle-Side Theorems

E N D

### Presentation Transcript

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. 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. 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.

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.

5. 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. O Reason J M Statement K 1. 2. 3. 4. 5. 6. 7. 8. 1. 2. 3. 4. 5. 6. 7. 8.

7. 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.

8. D Given: Prove: E H F G 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

More Related