Question

which statements are true about similar triangles?
corresponding angles are congruent.
their areas are equal.
they must be equilateral.
corresponding sides are proportional.
corresponding sides are congruent.

Explanation:

• Corresponding angles are congruent: By the definition of similar triangles, their corresponding angles are equal (congruent).
• Corresponding sides are proportional: This is a key property of similar triangles. If two triangles are similar, the ratios of their corresponding side lengths are equal.
• Their Areas are equal: Similar triangles have areas that are in the ratio of the square of the ratio of their corresponding side lengths. Only congruent triangles (a special case of similar triangles with ratio \(1:1\)) have equal areas.
• They must be equilateral: Similar triangles can be of various types (isosceles, scalene etc.), not just equilateral.
• Corresponding sides are congruent: This is a property of congruent triangles. For similar triangles, sides are proportional, not necessarily congruent.

Answer:

Corresponding angles are congruent, Corresponding sides are proportional.