5. In the regular pentagon ABCDE the interior diagonal AC is drawn. What is the degree measure of angle ZACD?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**THEOREM 4.7:**  
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

**Diagram Explanation:**  
There are two images of the same triangle labeled \( \triangle ABC \). In the first image, angles \( \angle C \) and \( \angle A \) are marked as congruent (indicated by identical arc marks). In the second image, sides \( AB \) and \( CB \) are marked as congruent (indicated by identical tick marks). The notation below states "If \( \angle C \cong \angle A \), then \( \overline{AB} \cong \overline{CB} \)."

---

**THEOREM 4.5:**  
In an isosceles triangle, the angles opposite the congruent sides are congruent.

**Diagram Explanation:**  
There are two images of the same triangle labeled \( \triangle ABC \). In the first image, sides \( AB \) and \( CB \) are marked as congruent (indicated by identical tick marks). In the second image, angles \( \angle C \) and \( \angle A \) are marked as congruent (indicated by identical arc marks). The notation below states "If \( \overline{AB} \cong \overline{CB} \), then \( \angle C \cong \angle A \)."
Transcribed Image Text:**THEOREM 4.7:** If two angles of a triangle are congruent, then the sides opposite those angles are congruent. **Diagram Explanation:** There are two images of the same triangle labeled \( \triangle ABC \). In the first image, angles \( \angle C \) and \( \angle A \) are marked as congruent (indicated by identical arc marks). In the second image, sides \( AB \) and \( CB \) are marked as congruent (indicated by identical tick marks). The notation below states "If \( \angle C \cong \angle A \), then \( \overline{AB} \cong \overline{CB} \)." --- **THEOREM 4.5:** In an isosceles triangle, the angles opposite the congruent sides are congruent. **Diagram Explanation:** There are two images of the same triangle labeled \( \triangle ABC \). In the first image, sides \( AB \) and \( CB \) are marked as congruent (indicated by identical tick marks). In the second image, angles \( \angle C \) and \( \angle A \) are marked as congruent (indicated by identical arc marks). The notation below states "If \( \overline{AB} \cong \overline{CB} \), then \( \angle C \cong \angle A \)."
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 \( \angle ACD \)?
Transcribed Image Text: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 \( \angle ACD \)?
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