Question

which statements must be true about the reflection of △xyz across mn? select three options. m∠xzy = 90° m∠mcy = 90° xx ≅ yy bz ≅ bz xy || xy

Explanation:

Step1: Recall reflection properties

A reflection is a rigid - motion. Rigid motions preserve angle measures and segment lengths.

Step2: Analyze angle measures

The measure of an angle in a figure and its reflection are equal. So, if in $\triangle XYZ$, $m\angle XZY = 90^{\circ}$, then in its reflection $\triangle X'Z'Y'$, $m\angle X'Z'Y'=90^{\circ}$.

Step3: Analyze segment lengths

A point and its image are equidistant from the line of reflection. Point $Z$ and its image $Z'$ are equidistant from the line of reflection $\overleftrightarrow{MN}$, so $\overline{BZ'}\cong\overline{BZ}$.

Step4: Analyze parallel lines

Corresponding sides of a figure and its reflection are parallel. So, $\overline{XY}\parallel\overline{X'Y'}$.

Answer:

$m\angle X'Z'Y' = 90^{\circ}$, $\overline{BZ'}\cong\overline{BZ}$, $\overline{XY}\parallel\overline{X'Y'}$