Question

which statements must be true about the reflection of △xyz across line l? 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

Since reflection preserves angle measures, if in $\triangle XYZ$, $\angle XZY = 90^{\circ}$, then in its reflection $\triangle X'Z'Y'$, $m\angle X'Z'Y'=90^{\circ}$. Also, the line of reflection $\overleftrightarrow{MN}$ is perpendicular to the segments connecting pre - image and image points. But there is no information to suggest $m\angle MCY = 90^{\circ}$.

Step3: Analyze segment lengths

The segments connecting pre - image and image points ($XX'$ and $YY'$) are not necessarily equal. However, a point and its image are equidistant from the line of reflection. So, $BZ = BZ'$.

Step4: Analyze parallelism

In a reflection, corresponding sides of the pre - image and image are parallel. So, $XY\parallel X'Y'$.

Answer:

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