Explain why all equilateral triangles must be similar.
Choose the correct answer below.
A. Since all sides of an equilateral triangle are the same and each angle is 60°, all equilateral triangles must be similar.
B. Since two sides of an equilateral triangle are the same, all equilateral triangles must be similar
The Correct Answer and Explanation is:
Correct Answer: A.
Since all sides of an equilateral triangle are the same and each angle is 60°, all equilateral triangles must be similar.
Explanation
In geometry, two shapes are similar if they have the same shape but not necessarily the same size. This means that corresponding angles are equal, and corresponding sides are in proportion (i.e., their lengths have the same ratio).
An equilateral triangle is a special type of triangle where all three sides are equal in length and all three interior angles are equal, each measuring exactly 60 degrees. This definition holds true for every equilateral triangle, regardless of its size.
Now, to understand why all equilateral triangles are similar, let’s apply the definition of similarity:
- Equal Corresponding Angles:
Every equilateral triangle has internal angles of 60°, so if we compare any two equilateral triangles, each of their angles (angle A, B, and C) matches the corresponding angles of the other triangle exactly. This satisfies the angle condition for similarity. - Proportional Corresponding Sides:
Although different equilateral triangles may have different side lengths (for example, one might have sides of 3 cm and another 6 cm), the ratios of their corresponding sides are always equal. That means the side of one triangle divided by the corresponding side of another gives a constant ratio across all three sides.
Because both conditions for similarity—equal angles and proportional sides—are satisfied automatically by the definition of equilateral triangles, all equilateral triangles are similar to each other.
Option B is incorrect because it mentions only “two sides being the same,” which describes an isosceles triangle, not an equilateral one. Isosceles triangles do not necessarily have all angles or all sides equal, so they are not always similar.
Hence, the correct and complete justification is given in Option A.
