Question

If two corresponding interior angles of two triangles are congruent, how do you know that the triangles are similar?(1 point) Responses 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. 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. 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 SAS criterion. Since two corresponding interior angles are congruent, the sides opposite the angles are congruent. The triangles are similar by SAS criterion. 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. Skip to navigation

Answer 1

If two corresponding interior angles of two triangles are congruent, we can conclude that the triangles are similar based on the Angle-Angle (AA) criterion for triangle similarity. Specifically:

Since two corresponding interior angles are congruent, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Consequently, the third angle of each triangle must also be congruent because the two angles give the rest of the angle measure in both triangles. Therefore, all three corresponding angles in the triangles are congruent.

Because all three corresponding angles of the triangles are congruent, the triangles are similar by the definition of similarity.

So, the correct response would be something like: "Since two corresponding interior angles are congruent, the sum of the angle measures in a triangle is 180°, which means the third angle pair must also be congruent. Because all three corresponding interior angles of the triangles are congruent, the triangles are similar by the definition of similarity."