Question

which statements must be true about the image of △mnp after a reflection across 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. 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:

Step1: Recall reflection properties

A reflection is a rigid - motion. Rigid - motions preserve congruence. So, the image of $\triangle MNP$ after reflection across $\overleftrightarrow{EG}$ will be congruent to $\triangle MNP$.

Step2: Analyze orientation

A reflection changes the orientation of a figure. So, the orientation of the image is not the same as the orientation of $\triangle MNP$.

Step3: Understand perpendicularity

The line of reflection $\overleftrightarrow{EG}$ is perpendicular to the line segments connecting the corresponding vertices of the pre - image and the image.

Step4: Examine line - segment congruence

The line segments connecting the corresponding vertices of the pre - image and the image are all congruent to each other.

Step5: Check parallelism

The line segments connecting the corresponding vertices of the pre - image and the image are all parallel to each other.

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 the corresponding vertices will all be congruent to each other.
The line segments connecting corresponding vertices will all be parallel to each other.