Which criterion states that if an angle of one triangle is congruent to the corresponding angle of another triangle and the including sides are proportional, the triangles are similar?

Which criterion states that if an angle of one triangle is congruent to the corresponding angle of another triangle and the including sides are proportional, the triangles are similar?

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

Answer: (B)

SAS similarity states that if one angle of a triangle equals the corresponding angle in another triangle and the sides that form that angle are in proportion, the two triangles are similar. The equal angle fixes the orientation, and the proportional including sides give the same scale factor for those adjacent sides, which forces all corresponding sides and angles to match up. It’s not about two angles being equal (that’s AA), or all three sides being in proportion (that’s SSS), and HL is a congruence criterion for right triangles, not a general similarity criterion. So the described condition matches SAS similarity.

SAS similarity states that if one angle of a triangle equals the corresponding angle in another triangle and the sides that form that angle are in proportion, the two triangles are similar. The equal angle fixes the orientation, and the proportional including sides give the same scale factor for those adjacent sides, which forces all corresponding sides and angles to match up. It’s not about two angles being equal (that’s AA), or all three sides being in proportion (that’s SSS), and HL is a congruence criterion for right triangles, not a general similarity criterion. So the described condition matches SAS similarity.