Question

which statements must be true about the image of △mnp after a reflection across (overleftrightarrow{eg})? select three options. the image will be congruent to △mnp. the orientation of the image will be the same as the orientation of △mnp. (overleftrightarrow{eg}) will be perpendicular to the line segments connecting the corresponding vertices. the line segments connecting the corresponding vertices will all be congruent to each other. the line segments connecting corresponding vertices will all be parallel to each other.

Explanation:

1. A reflection is a rigid - motion transformation. Rigid - motion transformations preserve congruence, so the image of $\triangle MNP$ will be congruent to $\triangle MNP$.
2. The line of reflection ($\overleftrightarrow{EG}$) is perpendicular to the line segments connecting corresponding vertices. This is a property of reflections.
3. The line segments connecting corresponding vertices are parallel to each other. This is also a property of reflections. The orientation of the image is reversed compared to the pre - image in a reflection, so the statement about the orientation being the same is false.

Answer:

The image will be congruent to $\triangle MNP$.
$\overleftrightarrow{EG}$ will be perpendicular to the line segments connecting the corresponding vertices.
The line segments connecting corresponding vertices will all be parallel to each other.