Which of the following is a true statement?

Options

A. Two similar triangles are always congruent.
B. Two similar triangles have equal areas
C. Two triangles are similar if their corresponding sides are proportional.
D. Two polygons are similar if their corresponding sides are proportional.

Answer

To solve the question, we need to evaluate each of the statements provided and determine which one is true. Let's analyze them one by one.

### Step-by-Step Solution:

1. **Statement 1: Two similar triangles are always congruent.**
- This statement is **false**. Similar triangles have the same shape but can be of different sizes. They have proportional sides but are not necessarily congruent (which means they are the same size and shape).

2. **Statement 2: Two similar triangles have equal areas.**
- This statement is also **false**. While similar triangles have proportional sides, their areas can differ based on the scale factor. Only congruent triangles have equal areas.

3. **Statement 3: Two triangles are similar if their corresponding sides are proportional.**
- This statement is **true**. The definition of similar triangles states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

4. **Statement 4: Two polygons are similar if their corresponding sides are proportional.**
- This statement is **true** as well. Similar polygons have their corresponding sides in proportion, but this statement does not directly relate to triangles specifically.

### Conclusion:
The true statement among the options is:
- **Statement 3: Two triangles are similar if their corresponding sides are proportional.**