Question

Triangle M N P and a line of reflection E G is shown.
Which statements must be true about the image of ΔMNP after a reflection across Line E G? Select three options.

The image will be congruent to ΔMNP.
The orientation of the image will be the same as the orientation of ΔMNP.
Line E G 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 1

Select:
- The image will be congruent to ΔMNP.
- Line 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.

Why: A reflection is an isometry so it preserves distance (congruence). Each original point and its image lie on a segment perpendicular to the mirror, with the mirror bisecting that segment, so those segments are perpendicular to EG. Since all those segments are perpendicular to the same line EG, they are parallel to each other. (Reflection reverses orientation, and the lengths of those connecting segments need not be equal to one another.)