Question

which statements are true? check all that apply.
the corresponding sides of similar triangles have proportional lengths.
the corresponding sides of congruent triangles have the same lengths.
the corresponding angles of similar triangles have different measures.
if corresponding sides of two triangles are not the same length, the triangles are not similar.
if corresponding sides of two triangles are not the same length, the triangles are not congruent.

Explanation:

• Similar triangles: By definition, corresponding sides are proportional. Corresponding angles are equal.
• Congruent triangles: By definition, corresponding sides are equal.
• For the statement “If corresponding sides of two triangles are not the same length, the triangles are not similar”: Similar triangles just need proportional sides, not equal.
• For the statement “If corresponding sides of two triangles are not the same length, the triangles are not congruent”: Congruent triangles require equal corresponding sides.

Answer:

• The corresponding sides of similar triangles have proportional lengths.
• The corresponding sides of congruent triangles have the same lengths.
• If corresponding sides of two triangles are not the same length, the triangles are not congruent.