Question
Based on the info given in the picture, how do you know that the triangles are similar?
(1 point)
Responses
We know that the sum of the measures of the angles in a triangle is 180 degrees, so the 3rd angle pair must have the same measure and therefore are congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.
We know that the sum of the measures of the angles in a triangle is 180 degrees, so the 3rd angle pair must have the same measure and therefore are congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.
We know that the sum of the measures of the angles in a triangle is 360 degrees, so the 3rd angle pair must have the same measure and therefore are congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.
We know that the sum of the measures of the angles in a triangle is 360 degrees, so the 3rd angle pair must have the same measure and therefore are 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. So 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. So 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. So the triangles are similar by the SSS criterion.
(1 point)
Responses
We know that the sum of the measures of the angles in a triangle is 180 degrees, so the 3rd angle pair must have the same measure and therefore are congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.
We know that the sum of the measures of the angles in a triangle is 180 degrees, so the 3rd angle pair must have the same measure and therefore are congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.
We know that the sum of the measures of the angles in a triangle is 360 degrees, so the 3rd angle pair must have the same measure and therefore are congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.
We know that the sum of the measures of the angles in a triangle is 360 degrees, so the 3rd angle pair must have the same measure and therefore are 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. So 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. So 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. So the triangles are similar by the SSS criterion.
Answers
Answered by
GPT-4o mini
The correct response is:
**We know that the sum of the measures of the angles in a triangle is 180 degrees, so the 3rd angle pair must have the same measure and therefore are congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.**
This response correctly identifies that the triangles are similar due to the Angle-Angle (AA) criterion for triangle similarity, where if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. Note that the sum of the angles in a triangle is 180 degrees, not 360 degrees, which is why the other responses are incorrect.
**We know that the sum of the measures of the angles in a triangle is 180 degrees, so the 3rd angle pair must have the same measure and therefore are congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.**
This response correctly identifies that the triangles are similar due to the Angle-Angle (AA) criterion for triangle similarity, where if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. Note that the sum of the angles in a triangle is 180 degrees, not 360 degrees, which is why the other responses are incorrect.