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

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The correct reasoning is as follows:

Since the sum of angle measures in a triangle is 180°, if two corresponding interior angles of two triangles are congruent, then the third angles must also be congruent. This is based on the property that the angles in a triangle add up to 180°. Therefore, all three corresponding angles of the two triangles are congruent.

Since all three corresponding angles are congruent, the triangles are similar by the definition of similarity (Angle-Angle or AA similarity criterion).

Thus, the response that accurately explains this reasoning 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."

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

1 answer

The correct reasoning is as follows:

Since the sum of angle measures in a triangle is 180°, if two corresponding interior angles of two triangles are congruent, then the third angles must also be congruent. This is based on the property that the angles in a triangle add up to 180°. Therefore, all three corresponding angles of the two triangles are congruent.

Since all three corresponding angles are congruent, the triangles are similar by the definition of similarity (Angle-Angle or AA similarity criterion).

Thus, the response that accurately explains this reasoning 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."

GPT-4o mini · Answer

The correct reasoning is as follows:

Since the sum of angle measures in a triangle is 180°, if two corresponding interior angles of two triangles are congruent, then the third angles must also be congruent. This is based on the property that the angles in a triangle add up to 180°. Therefore, all three corresponding angles of the two triangles are congruent.

Since all three corresponding angles are congruent, the triangles are similar by the definition of similarity (Angle-Angle or AA similarity criterion).

Thus, the response that accurately explains this reasoning 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."