Given: m∠B = 46°; m∠C = 45°; m∠R = 46°; m∠T = 89°

Prove: △ABC ~ △TRS

Triangles A B C and T R S are shown. Angles A B C and T R S are 46 degrees. Angle B C A is 45 degrees. Angle R T S is 89 degrees.

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