Help with problems 4 & 5 please? ### MATH 3713 - Fall 2020#### Homework 3**Due: 11-11 at the beginning of class**1. Complete problem #22 on page 235.2. Solve problem #25 in Section 5.2.3. Solve problem #26 in Section 5.2.4. **Problem**: Prove that in an isosceles triangle, the angle bisectors of the congruent angles are congruent. *For problem 4, you can certainly use the results already established back in Chapter 4, specifically Theorems 4.5 and 4.7.*5. In the regular pentagon $ ABCDE $, the interior diagonal $ AC $ is drawn. What is the degree measure of angle $ \angle ACD $? **Theorem 4.7**If two angles of a triangle are congruent, then the sides opposite those angles are congruent.*Diagram Explanation*: The diagram shows two triangles. In the first triangle, angle $ \angle C $ is congruent to angle $ \angle A $. In the second triangle, it is shown that side $ AB $ is congruent to side $ CB $.**Statement**: If $ \angle C \cong \angle A $, then $ AB \cong CB $.---**Theorem 4.5**In an isosceles triangle, the angles opposite the congruent sides are congruent.*Diagram Explanation*:The diagram shows an isosceles triangle where side $ AB $ is congruent to side $ CB $. The second part of the diagram shows that angle $ \angle C $ is congruent to angle $ \angle A $.**Statement**: If $ AB \cong CB $, then $ \angle C \cong \angle A $.

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4. Problem: Prove that in an isosceles triangle the angle bisectors of the congruent angles are congruent.

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Help with problems 4 & 5 please?

### MATH 3713 - Fall 2020
#### Homework 3

**Due: 11-11 at the beginning of class**

1. Complete problem #22 on page 235.
2. Solve problem #25 in Section 5.2.
3. Solve problem #26 in Section 5.2.
4. **Problem**: Prove that in an isosceles triangle, the angle bisectors of the congruent angles are congruent.
*For problem 4, you can certainly use the results already established back in Chapter 4, specifically Theorems 4.5 and 4.7.*
5. In the regular pentagon $ ABCDE $, the interior diagonal $ AC $ is drawn. What is the degree measure of angle $ \angle ACD $?

**Theorem 4.7**

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

*Diagram Explanation*:
The diagram shows two triangles. In the first triangle, angle $ \angle C $ is congruent to angle $ \angle A $. In the second triangle, it is shown that side $ AB $ is congruent to side $ CB $.

**Statement**: If $ \angle C \cong \angle A $, then $ AB \cong CB $.

---

**Theorem 4.5**

In an isosceles triangle, the angles opposite the congruent sides are congruent.

*Diagram Explanation*:
The diagram shows an isosceles triangle where side $ AB $ is congruent to side $ CB $. The second part of the diagram shows that angle $ \angle C $ is congruent to angle $ \angle A $.

**Statement**: If $ AB \cong CB $, then $ \angle C \cong \angle A $.

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