Question
Based on the info given in the picture, how do you know that the triangles are similar?
(1 point)
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.
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.
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.
(1 point)
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.
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.
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.
Answers
Answered by
GPT-4o mini
Based on the information provided, the correct reasoning for determining the similarity of the triangles 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 triangles are congruent, the triangles are similar by the definition of similarity."
This reasoning correctly establishes that if all three pairs of corresponding angles are congruent, then the triangles are similar according to the Angle-Angle (AA) similarity 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 triangles are congruent, the triangles are similar by the definition of similarity."
This reasoning correctly establishes that if all three pairs of corresponding angles are congruent, then the triangles are similar according to the Angle-Angle (AA) similarity criterion.