which statements must be true about the image of △mnp after a reflection across (overrightarrow{eg})? select…

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

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

Answer

Explanation:

Step1: Recall reflection properties

A reflection is a rigid - motion. Rigid motions preserve size and shape, so the image of a figure after reflection is congruent to the original figure. So, the image of $\triangle MNP$ will be congruent to $\triangle MNP$.

Step2: Analyze orientation

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

Step3: Consider line of reflection

The line of reflection ($\overleftrightarrow{EG}$) is perpendicular to the line segments connecting the corresponding vertices. This is a property of reflections.

Step4: Examine line - segments between vertices

The line segments connecting the corresponding vertices are congruent to each other. This is because a reflection is an isometry.

Step5: Check parallelism

The line segments connecting the corresponding vertices are perpendicular to the line of reflection, not 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.