Question
Which statement correctly explains the criterion that proves the triangles are similar? (1 point) Responses SSS because the two side lengths of AD to AB and DE to BC are proportional, meaning the other side length is also proportional. SSS because the two side lengths of AD to AB and DE to BC are proportional, meaning the other side length is also proportional. SAS because the given side lengths AD to AB and DE to BC are proportional; additionally, angle B is the same measure as angle D when translated SAS because the given side lengths AD to AB and DE to BC are proportional; additionally, angle B is the same measure as angle D when translated AA because all three angles are similar since the two angles at angle A are the same.
Answers
GPT-4o mini
To determine the similarity of triangles based on given conditions, we need to consider the criteria for triangle similarity: Side-Side-Side (SSS), Side-Angle-Side (SAS), and Angle-Angle (AA).
From the responses provided:
1. **SSS (Side-Side-Side)** states that if all three corresponding sides of two triangles are proportional, then the triangles are similar. This response mentions that two pairs of sides (AD to AB and DE to BC) are proportional, but it doesn't confirm that all three pairs of sides are proportional.
2. **SAS (Side-Angle-Side)** states that if two sides of one triangle are in proportion to two sides of another triangle and the angles included between those sides are equal, then the triangles are similar. The statement indicates that the side lengths are proportional and that angle B is equal to angle D, which fits this criterion if the sides correspond properly.
3. **AA (Angle-Angle)** states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. The response claims that "all three angles are similar" based on information about angle A, but does not provide specific information about the other angles.
Given the explanations, the most accurate criterion for proving similarity based on the information provided, specifically mentioning a proportional relationship and an included angle being equal, is **SAS**. Thus, the best response would be:
"SAS because the given side lengths AD to AB and DE to BC are proportional; additionally, angle B is the same measure as angle D when translated."
From the responses provided:
1. **SSS (Side-Side-Side)** states that if all three corresponding sides of two triangles are proportional, then the triangles are similar. This response mentions that two pairs of sides (AD to AB and DE to BC) are proportional, but it doesn't confirm that all three pairs of sides are proportional.
2. **SAS (Side-Angle-Side)** states that if two sides of one triangle are in proportion to two sides of another triangle and the angles included between those sides are equal, then the triangles are similar. The statement indicates that the side lengths are proportional and that angle B is equal to angle D, which fits this criterion if the sides correspond properly.
3. **AA (Angle-Angle)** states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. The response claims that "all three angles are similar" based on information about angle A, but does not provide specific information about the other angles.
Given the explanations, the most accurate criterion for proving similarity based on the information provided, specifically mentioning a proportional relationship and an included angle being equal, is **SAS**. Thus, the best response would be:
"SAS because the given side lengths AD to AB and DE to BC are proportional; additionally, angle B is the same measure as angle D when translated."