Introduction:
In geometry, two triangles are said to be similar if their corresponding angles are equal. This means that the corresponding sides of the triangles are in proportion. However, it is important to note that having equal corresponding angles does not necessarily mean that the triangles are congruent. Congruent triangles have all corresponding sides and angles equal.

Assertion: In two triangles, if corresponding angles are equal then the triangles are similar.

Reason: If the areas of two similar triangles are equal, then the triangles are congruent.

Explanation:

1. Corresponding Angles:
When two triangles have equal corresponding angles, it implies that the shapes of the triangles are similar. This is because angles are one of the defining characteristics of a shape, and if they match in both triangles, then the shapes are similar.

2. Similarity of Triangles:
Similarity of triangles is based on the concept of corresponding sides and angles. If two triangles have equal corresponding angles, then their corresponding sides are in proportion. This means that the ratio of the lengths of the corresponding sides in both triangles is equal. For example, if the ratio of the lengths of the corresponding sides in triangle ABC and triangle DEF is 1:2, then the triangles are similar.

3. Equal Area:
If two triangles are similar, then their areas are proportional to the square of the ratio of their corresponding sides. This means that if the ratio of the lengths of the corresponding sides of two similar triangles is 1:2, then the ratio of their areas will be 1:4. Conversely, if the areas of two similar triangles are equal, then the ratio of their corresponding sides is 1:1. Since congruent triangles have all corresponding sides and angles equal, if the areas of two similar triangles are equal, then the triangles must be congruent.

Conclusion:
In conclusion, the assertion that if corresponding angles of two triangles are equal, then the triangles are similar is true. However, the reason that if the areas of two similar triangles are equal, then the triangles are congruent is false. Similar triangles have equal corresponding angles, but congruent triangles have all corresponding sides and angles equal.