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The problem asks two parts about the given triangles:

1. **Are the triangles \( \triangle ABC \) and \( \triangle PQR \) equal?**
2. **If so, what is the ratio of the equal angles?**

I will go through each part step by step and provide a solution.

1. **Given Data**:
   - For \( \triangle ABC \):
     - \( AB = 5 \, \text{cm} \)
     - \( AC = 6 \, \text{cm} \)
     - \( \angle A = 50^\circ \)
   - For \( \triangle PQR \):
     - \( PQ = 5 \, \text{cm} \)
     - \( PR = 6 \, \text{cm} \)
     - \( \angle P = 50^\circ \)

2. **Are \( \triangle ABC \) and \( \triangle PQR \) congruent?**
   - The two triangles share the same side lengths for two sides and the angle between them. 
   - Based on the **SAS (Side-Angle-Side) Congruence Rule**, the triangles are congruent since:
     \[
     AB = PQ, \, AC = PR, \, \text{and} \, \angle A = \angle P = 50^\circ
     \]
   
3. **Ratio of Equal Angles**:
   Since the triangles are congruent, all corresponding angles will be equal. Therefore, the ratio of the angles is simply \( 1:1 \) for all the corresponding pairs of angles.

If you have any further questions or need details on any part of this solution, feel free to ask! Here's a set of additional practice questions related to this topic:

1. How do you prove two triangles are similar?
2. What are the criteria for triangle congruence besides SAS?
3. How do you find the area of congruent triangles?
4. Can two triangles with only equal angles be congruent?
5. How do the side ratios of similar triangles relate to their angles?

**Tip**: Always check for congruence criteria when comparing two triangles!

In △ABC, AB = 5 cm, AC = 6 cm, ∠A = 50°. In △PQR, PQ = 5 cm, PR = 6 cm and ∠P = 50°. (a) Are the triangles ABC and PQR equal? (b) If so, what is the ratio of equal angles?

Explore the solution to the problem involving triangles ABC and PQR, where you determine if the triangles are congruent using the SAS theorem and calculate the ratio of equal angles. Suitable for Grades 8-10 students.

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