If two triangles are similar, what is true about their corresponding sides?

• A. Perimeters are equal.
• B. Areas are equal.
• C. Congruent sides.
• D. Sides are in proportion.

Answer: (D)

When two triangles are similar, they have the same shape but possibly different sizes. This means every corresponding side length scales by a single constant factor. In other words, there exists a number k such that each side of one triangle is k times the length of its corresponding side in the other triangle, so all three pairs of corresponding sides are in the same proportion.

For example, if one triangle has side lengths 3, 4, and 5, a similar triangle could have 6, 8, and 10—the ratios are all 2. That uniform scaling shows why the sides are in proportion.

Perimeters would be equal only if the scale factor is 1 (the triangles are congruent), and areas would be equal only if the scale factor is 1 as well (since area scales by k^2). Congruent sides would mean the corresponding lengths are actually equal, which isn’t required by similarity—only their ratios must be the same.