Question

δpqr is dilated from the origin at a scale factor of $\frac{1}{2}$ to create δpqr. select the option that completes the statement: the triangles are ______ because their corresponding sides are ____ and their corresponding angles are ______. congruent; similar; proportional congruent; proportional; similar similar; congruent; proportional similar; proportional; congruent

Explanation:

Step1: Recall dilation property

Dilation creates similar figures.

Step2: Analyze side - length relationship

When a figure is dilated, corresponding sides are proportional. For example, if the scale factor is $k$, the ratio of corresponding side - lengths of the original and dilated figures is $k$. Here $k=\frac{1}{2}$, so corresponding sides of $\triangle PQR$ and $\triangle P'Q'R'$ are proportional.

Step3: Analyze angle - measure relationship

Dilation preserves angle measures. So corresponding angles of $\triangle PQR$ and $\triangle P'Q'R'$ are congruent.

Answer:

D. similar; proportional; congruent