Question

triangle def is reflected over the y - axis, and then translated down 4 units and right 3 units. which congruency statement describes the figures?
△def≅△sur
△def≅△sru
△def≅△rsu
△def≅△rus

Explanation:

Step1: Recall transformation properties

Reflections and translations are rigid - motions. Rigid - motions preserve the shape and size of a figure, so the pre - image and the image are congruent. The order of the vertices in the congruency statement must match the corresponding vertices.

Step2: Identify corresponding vertices

When we perform the given transformations on $\triangle DEF$ (reflection over the $y$ - axis, translation down 4 units and right 3 units), we can match the vertices of $\triangle DEF$ with the vertices of the new triangle. By observing the graph, we can see that $D$ corresponds to $S$, $E$ corresponds to $R$, and $F$ corresponds to $U$. So the congruency statement is $\triangle DEF\cong\triangle SRU$.

Answer:

$\triangle DEF\cong\triangle SRU$