Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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### Congruent Triangles

**Triangles ABC and PQR are congruent:**

![Triangles ABC and PQR](URL-to-image)

*Diagram Explanation:*
- The diagram shows two triangles. Triangle ABC has vertices labeled as A, B, and C. Triangle PQR has vertices labeled as P, Q, and R.

**Question:**
Which statement about the triangles is true?

**Options:**
- A) \( \angle A \cong \angle R \)
- B) \( \angle C \cong \angle R \)
- C) \( \overline{AB} \cong \overline{RQ} \)
- D) \( \overline{CB} \cong \overline{PQ} \)

**Explanation:**
Given that triangles ABC and PQR are congruent, it implies that their corresponding angles and sides are equal:
- \( \angle A \cong \angle P \)
- \( \angle B \cong \angle Q \)
- \( \angle C \cong \angle R \)
- \( \overline{AB} \cong \overline{PQ} \)
- \( \overline{BC} \cong \overline{QR} \)
- \( \overline{CA} \cong \overline{RP} \)

Therefore, the correct statement among the given options is B) \( \angle C \cong \angle R \).
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Transcribed Image Text:### Congruent Triangles **Triangles ABC and PQR are congruent:** ![Triangles ABC and PQR](URL-to-image) *Diagram Explanation:* - The diagram shows two triangles. Triangle ABC has vertices labeled as A, B, and C. Triangle PQR has vertices labeled as P, Q, and R. **Question:** Which statement about the triangles is true? **Options:** - A) \( \angle A \cong \angle R \) - B) \( \angle C \cong \angle R \) - C) \( \overline{AB} \cong \overline{RQ} \) - D) \( \overline{CB} \cong \overline{PQ} \) **Explanation:** Given that triangles ABC and PQR are congruent, it implies that their corresponding angles and sides are equal: - \( \angle A \cong \angle P \) - \( \angle B \cong \angle Q \) - \( \angle C \cong \angle R \) - \( \overline{AB} \cong \overline{PQ} \) - \( \overline{BC} \cong \overline{QR} \) - \( \overline{CA} \cong \overline{RP} \) Therefore, the correct statement among the given options is B) \( \angle C \cong \angle R \).
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