if two corresponding interior angles of two triangles are congruent, how do you know that the triangles are similar?

Question

a. since the sum of angle measures in a triangle is 360*, the third angle pair must have the same measure and are thus congruent. because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity
b. since the sum of angle measures in a triangle is 180*, the third angle pair must have the same measure and are thus congruent. because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity
c. since two corresponding interior angles are congruent, the sides opposite the angles are congruent. the remaining pair of sides must also be congruent. the triangles are similar by SSS criterion
d. since two corresponding interior angles are congruent, the sides opposite the angles are congruent. the triangles are similar by SAS criterion

Answer 1

The correct reason for why two triangles are similar if two corresponding interior angles are congruent is:

b. since the sum of angle measures in a triangle is 180°, the third angle pair must have the same measure and are thus congruent. because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.

This option correctly states that the sum of the angles in a triangle is 180 degrees, which leads to the conclusion that the third angles are also congruent. As a result, all three angles in the triangles are congruent, fulfilling the criteria for similarity (AA criterion: Angle-Angle similarity).