If `DeltaABC~=DeltaPRQ`, then `angleBandPQ` are respectively equal to

Options

A. `anglePandAC`
B. `angleRandBC`
C. `angleRandAC`
D. `angleQandAB`

Answer

To solve the problem, we need to use the concept of congruence of triangles. Given that triangle ABC is congruent to triangle PRQ (denoted as ΔABC ≅ ΔPRQ), we can conclude that their corresponding parts are equal.

### Step-by-Step Solution:

1. **Understanding Congruence**:
Since ΔABC ≅ ΔPRQ, it means that all corresponding sides and angles of these triangles are equal.

2. **Identifying Corresponding Parts**:
From the congruence, we can identify the corresponding parts:
- Side AB corresponds to side PR.
- Side BC corresponds to side RQ.
- Side AC corresponds to side PQ.
- Angle A corresponds to angle P.
- Angle B corresponds to angle R.
- Angle C corresponds to angle Q.

3. **Using CPCT**:
The acronym CPCT stands for "Corresponding Parts of Congruent Triangles". This means:
- AB = PR
- BC = RQ
- AC = PQ
- Angle A = Angle P
- Angle B = Angle R
- Angle C = Angle Q

4. **Finding the Required Angles and Sides**:
We need to find the measures of angle B and side PQ:
- From CPCT, we know that angle B = angle R.
- Also, from CPCT, we know that side PQ = side AC.

5. **Conclusion**:
Therefore, angle B is equal to angle R, and side PQ is equal to side AC.

### Final Answer:
- Angle B = Angle R
- Side PQ = Side AC