Question
A dilation with scale factor 0.25 is performed on triangle 1 to produce triangle 2. Which statement must be true about the two triangles?
Their corresponding sides have equal lengths, and their corresponding angles have equal measures.
Their corresponding sides are parallel, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
Their corresponding sides are parallel, and their corresponding angles have equal measures.
Their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
Their corresponding sides have equal lengths, and their corresponding angles have equal measures.
Their corresponding sides are parallel, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
Their corresponding sides are parallel, and their corresponding angles have equal measures.
Their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
Answers
GPT-4o mini
When a dilation is performed on a triangle, the resulting triangle is similar to the original triangle. Specifically, with a scale factor of 0.25, the following properties hold:
1. Corresponding angles of the two triangles are equal.
2. Corresponding sides of the two triangles are proportional, in this case with a ratio of 0.25 (meaning the sides of triangle 2 are 0.25 times the lengths of the corresponding sides of triangle 1).
Given this information, the correct statement regarding the two triangles would be:
**Their corresponding sides are parallel, and their corresponding angles have equal measures.**
This statement reflects the truth about similar triangles resulting from a dilation, where corresponding angles are equal, and the sides maintain a proportional relationship reflecting the scale factor.
1. Corresponding angles of the two triangles are equal.
2. Corresponding sides of the two triangles are proportional, in this case with a ratio of 0.25 (meaning the sides of triangle 2 are 0.25 times the lengths of the corresponding sides of triangle 1).
Given this information, the correct statement regarding the two triangles would be:
**Their corresponding sides are parallel, and their corresponding angles have equal measures.**
This statement reflects the truth about similar triangles resulting from a dilation, where corresponding angles are equal, and the sides maintain a proportional relationship reflecting the scale factor.