Question

given: m∠b = 46°; m∠c = 45°; m∠r = 46°; m∠t = 89°
prove: △abc ~ △trs
melissa believes that the aa similarity theorem can prove that the triangles are similar. which fact would be necessary in the proof?
× △abc is an acute triangle.
○ △trs is larger than △abc.
○ the sum of the measures of the interior angles of a triangle is 180°.
○ the sum of the side lengths of two sides of a triangle is greater than the third side length.

Explanation:

Step1: Calculate ∠A in △ABC

Sum of angles in triangle = 180°.
∠A = 180° - ∠B - ∠C = 180° - 46° - 45° = 89°.

Step2: Calculate ∠S in △TRS

Sum of angles in triangle = 180°.
∠S = 180° - ∠R - ∠T = 180° - 46° - 89° = 45°.

Step3: Verify AA similarity

∠B = ∠R = 46°, ∠A = ∠T = 89°, ∠C = ∠S = 45°. AA similarity needs two equal angles, which requires knowing the angle sum theorem to find missing angles.

Answer:

The sum of the measures of the interior angles of a triangle is 180°.