If two corresponding interior angles of two triangles are congruent, how do you know that the triangles are similar?(7 points)

Question

Responses

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

Answer 1

The correct response would be:

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 triangles are congruent, the triangles are similar by the definition of similarity.

This reasoning correctly applies the property of triangle angle sums and the definition of triangle similarity. The statement about the sum being 360° is incorrect, as the total angle measure in a triangle is always 180°. The other options also either incorrectly reference congruence of sides or misapply similarity criteria (such as SAS or SSS) without following from the congruence of angles.