Question

question 6
which statements must be true about the image of △mnp after a reflection across eg? check all that apply.
a. the image will be congruent to △mnp.
b. the orientation of the image will be the same as the orientation of △mnp.
c. eg will be perpendicular to the line segments connecting the corresponding vertices.
d. the line segments connecting the corresponding vertices will all be congruent to each other.
e. the line segments connecting corresponding vertices will all be parallel to each other.

Explanation:

Step1: Recall properties of reflection

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 $\triangle MNP$, and statement a is true.

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 $\triangle MNP$, and statement b is false.

Step3: Consider the line of reflection

The line of reflection (EG) is perpendicular to the line segments connecting the corresponding vertices of the pre - image and the image. So, statement c is true.

Step4: Examine line segments between corresponding vertices

The line segments connecting the corresponding vertices of a pre - image and its reflection are congruent to each other and parallel to each other. So, statements d and e are true.

Answer:

a. The image will be congruent to $\triangle MNP$.
c. EG will be perpendicular to the line segments connecting the corresponding vertices.
d. The line segments connecting the corresponding vertices will all be congruent to each other.
e. The line segments connecting corresponding vertices will all be parallel to each other.