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

Correct choices:
- 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.

Reason: A reflection is an isometry, so the image is congruent but its orientation is reversed (so "same orientation" is false). For each vertex, the segment joining it to its reflected image is perpendicular to the mirror line (and the mirror bisects that segment), hence all those segments are perpendicular to EG and therefore parallel to each other. They need not be congruent to one another.