Question

triangle srq undergoes a rigid transformation that results in triangle vut. which statements are true regarding the transformation? select two options. sq corresponds to vu. ∠r corresponds to ∠u. uv corresponds to rs. ∠s corresponds to ∠t. qs corresponds to rs.

Explanation:

Step1: Recall rigid - transformation property

In a rigid transformation, corresponding angles and sides of the pre - image and image are congruent. The order of vertices in the naming of the triangles gives the correspondence. Since $\triangle SRQ$ is transformed to $\triangle VUT$, $S$ corresponds to $V$, $R$ corresponds to $U$, and $Q$ corresponds to $T$.

Step2: Check side - correspondence

For sides, $\overline{SQ}$ corresponds to $\overline{VT}$, $\overline{SR}$ corresponds to $\overline{VU}$, and $\overline{RQ}$ corresponds to $\overline{UT}$. For angles, $\angle S$ corresponds to $\angle V$, $\angle R$ corresponds to $\angle U$, and $\angle Q$ corresponds to $\angle T$.

Answer:

1. $\overline{SQ}$ corresponds to $\overline{VT}$ (not $\overline{VU}$, so this is false).
2. $\angle R$ corresponds to $\angle U$ (true).
3. $\overline{UV}$ corresponds to $\overline{RS}$ (true).
4. $\angle S$ corresponds to $\angle V$ (not $\angle T$, so this is false).
5. $\overline{QS}$ corresponds to $\overline{UT}$ (not $\overline{RS}$, so this is false).

So the two true statements are: $\angle R$ corresponds to $\angle U$, $\overline{UV}$ corresponds to $\overline{RS}$.