Question

which statements must be true about the image of δmnp after a reflection across eg? select three options. the image will be congruent to δmnp. the orientation of the image will be the same as the orientation of δmnp. 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 transformation. Rigid - motion transformations preserve size and shape. So, the image of a figure after reflection is congruent to the original figure. Thus, 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 of $\triangle MNP$ will not be the same as the orientation of $\triangle MNP$.

Step3: Consider line - segment properties

The line of reflection $\overleftrightarrow{EG}$ is perpendicular to the line segments connecting the corresponding vertices of the pre - image and the image. Also, the line segments connecting the corresponding vertices are congruent to each other and 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. (We can choose any three of the correct statements among these four correct ones. Commonly, we may choose the first three as answers)