Question

which triangle is \\( \triangle a b c \\) similar to and why?
\\( \triangle a b c \\) is similar to \\( \triangle d e f \\) by the aa similarity postulate
\\( \triangle a b c \\) is not similar to any of the triangles given.
\\( \triangle a b c \\) is similar to \\( \triangle g h i \\) by the aa similarity postulate
\\( \triangle a b c \\) is similar to \\( \triangle j k l \\) by the aa similarity postulate

Explanation:

Step1: Find angles of △ABC

In △ABC, ∠B = 65°, ∠C = 65°. So ∠A = 180° - 65° - 65° = 50°.

Step2: Analyze △DEF

In △DEF, ∠E = 65°, ∠D = 20°. ∠F = 180° - 65° - 20° = 95°. Angles don't match △ABC.

Step3: Analyze △GHI

In △GHI, ∠H = 65°, ∠G = 50°. ∠I = 180° - 65° - 50° = 65°. Angles: 50°, 65°, 65° match △ABC's angles (50°, 65°, 65°). By AA (two angles equal), they are similar.

Step4: Analyze △JKL

In △JKL, ∠K = 65°, ∠L = 60°. ∠J = 180° - 65° - 60° = 55°. Angles don't match △ABC.

Answer:

△ABC is similar to △GHI by the AA Similarity Postulate