Question

triangle def was dilated according to the rule $d_{o, \frac{1}{3}}$ $(x,y) \to \left( \frac{1}{3}x, \frac{1}{3}y \
ight)$ to create similar triangle def.
which statements are true? select three options.
$\square$ $\angle f$ corresponds to $\angle f$.
$\square$ segment ee is parallel to segment ff.
$\square$ the distance from point d to the origin is $\frac{1}{3}$ the distance of point d to the origin.
$\square$ the measure of $\angle e$ is $\frac{1}{3}$ the measure of $\angle e$.
$\square$ $\triangle def \sim \triangle def$

Explanation:

Step1: Check angle correspondence

Dilation preserves angle measures and correspondence; ∠F ↔ ∠F'.

Step2: Check distance ratio

Dilation by scale factor $\frac{1}{3}$ from origin: $OD' = \frac{1}{3}OD$.

Step3: Check similarity

Dilation creates similar figures: $\triangle DEF \sim \triangle D'E'F'$.

Answer:

∠F corresponds to ∠F', The distance from point D' to the origin is $\frac{1}{3}$ the distance of point D to the origin, △DEF ~ △D'E'F'