Question

In the following statements, the true statement is :

• A. All circles are congruent.
• B. All rectangles are similar.
• C. All equilateral triangles are similar.
• D. All polygons are similar.

Hint:

Regular polygons with the same number of sides (like all squares or all equilateral triangles) are always similar to each other.

Answer 1

The Correct Option is C

To determine which of the given statements is true, let's analyze each option:

1. Statement: All circles are congruent.
   Explanation: Circles are congruent if they have the same radius. However, circles can have different radii, which means not all circles are congruent. Therefore, this statement is false.
2. Statement: All rectangles are similar.
   Explanation: Rectangles are similar if the ratios of their corresponding sides are equal. While rectangles have four right angles, their side lengths can differ, meaning not all rectangles are similar. Therefore, this statement is false.
3. Statement: All equilateral triangles are similar.
   Explanation: Equilateral triangles have all sides equal and all angles measuring 60 degrees. Due to having identical angles, all equilateral triangles are similar by the Angle-Angle (AA) similarity criterion. This statement is true.
4. Statement: All polygons are similar.
   Explanation: For polygons to be similar, corresponding angles must be equal, and the sides should be in proportion. This is not true for all polygons, as they can have different angles and side lengths. Therefore, this statement is false.

Conclusion: Given the analysis, the correct statement is: All equilateral triangles are similar.