Question

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

Explanation:

Step1: Recall AA - Similarity Postulate

The AA (Angle - Angle) similarity postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

Step2: Analyze angles in \(\triangle ABC\)

In \(\triangle ABC\), two angles are \(65^{\circ}\). Using the angle - sum property of a triangle (\(A + B + C=180^{\circ}\)), the third angle is \(180-(65 + 65)=50^{\circ}\).

Step3: Analyze \(\triangle GHI\)

In \(\triangle GHI\), the angles are \(65^{\circ}\) and \(50^{\circ}\).

Step4: Check for AA - Similarity

\(\triangle ABC\) and \(\triangle GHI\) have two pairs of congruent angles (\(65^{\circ}\) and \(50^{\circ}\)). So, \(\triangle ABC\) is similar to \(\triangle GHI\) by the AA - Similarity Postulate.

Answer:

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