Question

amore is using a grid to create patterns for his kente cloth design. does amares first pattern show a dilation? complete the table. question yes or no are corresponding angles congruent? are corresponding sides proportional? is the pattern a dilation?

Explanation:

Step1: Recall dilation properties

In a dilation, corresponding angles of the pre - image and image are congruent because dilation is a similarity transformation. So for the question "Are corresponding angles congruent?", the answer is Yes.

Step2: Check side - length ratios

Count the grid units for corresponding sides. If we assume the smaller triangle is the pre - image and the larger one is the image, we can see that the ratio of the lengths of corresponding sides is constant. For example, if we consider the vertical sides of the two similar triangles, the ratio of their lengths is the same as the ratio of other corresponding sides. So for the question "Are corresponding sides proportional?", the answer is Yes.

Step3: Determine if it's a dilation

Since corresponding angles are congruent and corresponding sides are proportional, the pattern is a dilation. So for the question "Is the pattern a dilation?", the answer is Yes.

Answer:

Are corresponding angles congruent? Yes
Are corresponding sides proportional? Yes
Is the pattern a dilation? Yes