Question

question 1 - 26
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

Explanation:

Step1: Properties of dilation

A dilation is a transformation that changes the size of a figure but not its shape. When a dilation with scale factor \(k = 0.25\) is performed on a triangle (triangle 1) to get another triangle (triangle 2), the corresponding sides of the two triangles are parallel.

Step2: Angle - measure property in dilation

The measure of angles in a figure is not changed by dilation. So, the corresponding angles of triangle 1 and triangle 2 have equal measures.

Answer:

Their corresponding sides are parallel, and their corresponding angles have equal measures.