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

Step 1: Understanding the Concept:
Similarity in geometry means that shapes have the same shape but not necessarily the same size. For polygons to be similar, their corresponding angles must be equal and their corresponding sides must be in the same ratio.
Step 2: Analyzing Options:
- (a) Circles are congruent only if they have the same radius.
- (b) Rectangles can have different length-to-width ratios, so they aren't all similar.
- (c) All equilateral triangles have three $60^\circ$ angles, and their sides are always in a constant ratio.
- (d) Different polygons (like a pentagon and a hexagon) are obviously not similar.
Step 3: Conclusion:
All equilateral triangles are similar by the AAA (Angle-Angle-Angle) similarity criterion.
Step 4: Final Answer:
The true statement is (c).