Question

triangle uvw and triangle uvn are drawn below. if $overline{uv}congoverline{uv},overline{uw}congoverline{un}$, and $angle wuvcongangle nuv$, use the dropdown boxes below to determine a transformation that maps triangle uvw onto triangle uvn. then use a congruence statement to explain why this is possible.

Explanation:

Step1: Identify the transformation

Since $\angle WUV\cong\angle NUV$, we can use a reflection. Reflect $\triangle UVW$ over the line containing $\overrightarrow{UV}$. This will map $\triangle UVW$ onto $\triangle UVN$ because the angle - bisector (the line containing $\overrightarrow{UV}$ in this case) is the axis of symmetry for the two congruent triangles.

Step2: Write the congruence statement

We are given $\overline{UV}\cong\overline{UV}$ (reflexive property), $\overline{UW}\cong\overline{UN}$, and $\angle WUV\cong\angle NUV$. By the Side - Angle - Side (SAS) congruence criterion, $\triangle UVW\cong\triangle UVN$.

Answer:

The transformation is a reflection over the line containing $\overrightarrow{UV}$. The congruence statement is $\triangle UVW\cong\triangle UVN$ by SAS.