In `Delta ABC and Delta PQR` , If AB=AC, `angleC=angleP " and " angleB=angleQ,` then the two triangles are

Options

A. isosceles but not congruent
B. isosceles and congruent
C. congruent but not isosceles
D. Neither congruent nor isosceles

Explanation

To solve the problem, we need to analyze the given information about triangles ABC and PQR.

### Step-by-Step Solution:

1. **Identify Given Information**:
- We have two triangles: ΔABC and ΔPQR.
- It is given that AB = AC (sides of triangle ABC are equal).
- It is also given that ∠C = ∠P and ∠B = ∠Q.

2. **Determine the Type of Triangle ABC**:
- Since AB = AC, by the property of isosceles triangles, we know that the angles opposite to equal sides are equal. Therefore, ∠B = ∠C.
- This means triangle ABC is an isosceles triangle because it has at least two equal sides (AB and AC).

3. **Analyze the Angles**:
- We know that ∠C = ∠P and ∠B = ∠Q.
- Since ∠B = ∠Q (from the given information), we can conclude that ∠C = ∠P = ∠Q.

4. **Determine the Type of Triangle PQR**:
- Since ∠C = ∠P and ∠B = ∠Q, we can say that triangle PQR also has two equal angles (∠P and ∠Q).
- Therefore, triangle PQR is also an isosceles triangle.

5. **Conclusion**:
- Both triangles ABC and PQR are isosceles triangles because they each have at least two equal sides and two equal angles.
- However, we cannot conclude that the triangles are congruent because they do not share all three pairs of equal sides or angles (AAA does not guarantee congruence).

Thus, the final answer is that the two triangles are **isosceles**.