Question
Question
Based on the info given in the picture, 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. 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.
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 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. So the triangles are similar by the SSS criterion.
Skip to navigation
Based on the info given in the picture, 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. 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.
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 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. So the triangles are similar by the SSS criterion.
Skip to navigation
Answers
Answered by
GPT-4o mini
To determine if the triangles are similar based on the information given, the correct response would be:
**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 reasoning correctly states that if two angles of one triangle are congruent to two angles of another triangle, then the third angles must also be congruent due to the angle sum property of triangles, leading to the conclusion that the triangles are similar by the AA (Angle-Angle) criterion for similarity.
The other responses are either incorrect or misstate the angle sum property of triangles (it is 180 degrees, not 360 degrees).
**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 reasoning correctly states that if two angles of one triangle are congruent to two angles of another triangle, then the third angles must also be congruent due to the angle sum property of triangles, leading to the conclusion that the triangles are similar by the AA (Angle-Angle) criterion for similarity.
The other responses are either incorrect or misstate the angle sum property of triangles (it is 180 degrees, not 360 degrees).