Assertion (A): Two similar triangles are always congruent.
Reason (R ): It the area of two similar triangles are equal then the triangles are congruent

Options

A. Both A and R are true R is the correct explanation for A.
B. Both A and R are true nad R is not correct explanation for A.
C. A is true but R is false.
D. A is false but R is true.

Answer

To solve the given question, we need to analyze the assertion and reason provided:

**Assertion (A)**: Two similar triangles are always congruent.
**Reason (R)**: If the area of two similar triangles is equal, then the triangles are congruent.

### Step-by-Step Solution:

1. **Understanding Similar Triangles**:
- Similar triangles have the same shape but may differ in size. This means that their corresponding angles are equal, and the lengths of corresponding sides are in proportion.

2. **Analyzing Assertion (A)**:
- The assertion states that two similar triangles are always congruent. This is not true. For example, consider triangle ABC with sides 2, 3, and 4, and triangle DEF with sides 4, 6, and 8. These triangles are similar (the sides are in the ratio 1:2), but they are not congruent because their sides are not equal.

**Hint**: Remember that similarity does not imply congruence; it only implies proportionality of sides and equality of angles.

3. **Analyzing Reason (R)**:
- The reason states that if the areas of two similar triangles are equal, then the triangles are congruent. This is true. The area of similar triangles is proportional to the square of the ratio of their corresponding sides. If the areas are equal, the ratio of the sides must be 1:1, meaning the triangles must be congruent.

**Hint**: Recall the formula for the area of similar triangles: the ratio of their areas is equal to the square of the ratio of their corresponding sides.

4. **Conclusion**:
- Since assertion (A) is false (two similar triangles are not always congruent), and reason (R) is true (if the areas of two similar triangles are equal, then they are congruent), we conclude that:
- Assertion (A) is false.
- Reason (R) is true.

### Final Answer:
- Assertion (A) is false, and Reason (R) is true.