Which criterion states that if the three pairs of corresponding sides are proportional, the triangles are similar?

Which criterion states that if the three pairs of corresponding sides are proportional, the triangles are similar?

• A. SSS for Similarity
• B. SAS for Similarity
• C. AA Similarity
• D. HL Congruence

Answer: (A)

The idea being tested is SSS Similarity: if the three pairs of corresponding sides are in the same proportion, the triangles are similar. That means there’s a constant scale factor so each side of one triangle is a constant multiple of the corresponding side of the other. When all three side ratios match, the triangles have the same shape, so all corresponding angles are equal. This is different from SAS Similarity, which would require two sides in proportion and the included angle equal; AA Similarity, which needs two angles equal; and HL Congruence, which is a rule for right triangles to prove congruence, not similarity.

The idea being tested is SSS Similarity: if the three pairs of corresponding sides are in the same proportion, the triangles are similar. That means there’s a constant scale factor so each side of one triangle is a constant multiple of the corresponding side of the other. When all three side ratios match, the triangles have the same shape, so all corresponding angles are equal.

This is different from SAS Similarity, which would require two sides in proportion and the included angle equal; AA Similarity, which needs two angles equal; and HL Congruence, which is a rule for right triangles to prove congruence, not similarity.