Question

understanding congruence and similarity

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:

Analyze properties of similar triangles

• Similar triangles have proportional corresponding side lengths: True.
• Corresponding angles of similar triangles are equal, not different: False.
• Triangles can be similar even if their corresponding sides are not the same length (they are scaled versions): False.

Analyze properties of congruent triangles

• Congruent triangles have equal corresponding side lengths: True.
• If corresponding sides are not the same length, the triangles cannot be congruent: True.

Answer:

• The corresponding sides of similar triangles have proportional lengths. (Correct answer)
• The corresponding sides of congruent triangles have the same lengths. (Correct answer)
• 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. (Correct answer)