Question

quadrilateral abcd is dilated to create abcd. which three statements about the similar quadrilaterals are true? the scale factor used in the dilation is 2. (overline{dc}) is dilated by a scale factor of (\frac{1}{2}) to create (overline{dc}). angle b is half the size of angle b. angle a is both congruent and corresponding to angle a. the dilation is a reduction

Explanation:

Step1: Analyze scale - factor

Observe the lengths of corresponding sides. If we consider a side - length of the original quadrilateral and its corresponding side - length in the dilated quadrilateral, we can find the scale factor. Let's assume we look at a horizontal or vertical side. For example, if we consider a side of the larger quadrilateral and the corresponding side of the smaller one, we can see that the side - lengths of the smaller quadrilateral are half of the side - lengths of the larger one. So the scale factor of dilation is $\frac{1}{2}$. This means the dilation is a reduction.

Step2: Recall properties of dilation

In a dilation, corresponding angles are congruent. That is, for two similar figures (formed by dilation), $\angle A\cong\angle A'$, $\angle B\cong\angle B'$, $\angle C\cong\angle C'$, and $\angle D\cong\angle D'$.

Answer:

• $\overline{DC}$ is dilated by a scale factor of $\frac{1}{2}$ to create $\overline{D'C'}$.
• Angle A is both congruent and corresponding to angle A'.
• The dilation is a reduction.