f two corresponding interior angles of two triangles are congruent, how do you know that the triangles are similar?(1 point)

Question

Responses

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.
Since the sum of angle measures in a triangle is 360 degrees, 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.

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.
Since the sum of angle measures in a triangle is 180 degrees, 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.

Since two corresponding interior angles are congruent, the sides opposite the angles are congruent. The triangles are similar by SAS criterion.
Since two corresponding interior angles are congruent, the sides opposite the angles are congruent. The triangles are similar by SAS criterion.

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.

Answer 1

The correct response is:

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 explanation accurately reflects that in any triangle, the sum of the interior angles is always 180 degrees. If two angles of one triangle are congruent to two angles of another triangle, then the third angles must also be congruent, leading to all three angles being congruent. According to the Angle-Angle (AA) criterion for triangle similarity, this means the triangles are similar.