Question

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which triangle is $\triangle abc$ similar to and why?
note: figures are not drawn to scale.
$\triangle abc$ is similar to $\triangle ghi$ by aa similarity postulate.
$\triangle abc$ is similar to $\triangle jkl$ by aa similarity postulate.
$\triangle abc$ is similar to $\triangle def$ by aa similarity postulate.
$\triangle abc$ is not similar to any of the triangles given.

Explanation:

Step1: Find angles of △ABC

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

Step2: Analyze △GHI

In △GHI, ∠G = 50°, ∠H = 65°, so ∠I = 180° - 50° - 65° = 65°.

Step3: Apply AA Similarity

△ABC has angles 50°, 65°, 65°; △GHI has angles 50°, 65°, 65°. So two angles match (AA), so they are similar.
Check other options:

• △DEF: ∠D = 20°, ∠E = 65°, ∠F = 95° (not matching △ABC's angles).
• △JKL: ∠K = 65°, ∠L = 60°, ∠J = 55° (not matching).

Answer:

$\triangle ABC$ is similar to $\triangle GHI$ by AA Similarity Postulate.