In `triangle ABC` and `triangle` DEF, AB = DE, BC = EF and `angleB = angleE`. If the perimeter of `triangle` ABC is 20, then the perimeter of `triangle` DEF is ..........

Options

A. 10
B. 20
C. 15
D. 40

Answer

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

### Step-by-Step Solution:

1. **Identify the Given Information**:
- We have two triangles: ABC and DEF.
- The sides are given as follows:
- AB = DE
- BC = EF
- The angles are given as:
- ∠B = ∠E
- The perimeter of triangle ABC is given as 20.

2. **Understand the Congruency**:
- Since we have two sides and the included angle of triangle ABC equal to the corresponding two sides and included angle of triangle DEF, we can use the Side-Angle-Side (SAS) congruence criterion.
- By SAS congruence, we can conclude that triangle ABC is congruent to triangle DEF.

3. **Apply the Congruency**:
- From the congruence of triangles, we know that all corresponding sides of congruent triangles are equal.
- Therefore, we have:
- AC = DF (the third side of both triangles).

4. **Calculate the Perimeter of Triangle DEF**:
- The perimeter of a triangle is the sum of the lengths of its sides.
- For triangle ABC, the perimeter is:
\[ \text{Perimeter of ABC} = AB + BC + AC = 20 \]
- For triangle DEF, the perimeter is:
\[ \text{Perimeter of DEF} = DE + EF + DF \]
- Since AB = DE, BC = EF, and AC = DF, we can substitute:
\[ \text{Perimeter of DEF} = AB + BC + AC \]
- Therefore, the perimeter of triangle DEF is equal to the perimeter of triangle ABC:
\[ \text{Perimeter of DEF} = 20 \]

5. **Final Answer**:
- The perimeter of triangle DEF is **20**.