Question

which statements must be true about the image of δmnp after a reflection across \overleftrightarrow{eg}? select three options. \bigcirc the image will be congruent to δmnp. \bigcirc the orientation of the image will be the same as the orientation of δmnp. \bigcirc \overleftrightarrow{eg} will be perpendicular to the line segments connecting the corresponding vertices. \bigcirc the line segments connecting the corresponding vertices will all be congruent to each other. \bigcirc the line segments connecting corresponding vertices will all be parallel to each other.

Explanation:

• Reflection preserves congruence (shape/size), so the image ≅ ΔMNP.
• Reflection reverses orientation (flips the figure), so orientation differs.
• The line of reflection (EG) is perpendicular to segments connecting corresponding vertices (reflection property).
• Segments connecting corresponding vertices have lengths equal to twice the distance from each vertex to EG, which vary unless vertices are equidistant to EG (not guaranteed).
• Segments connecting corresponding vertices are all perpendicular to EG, so they are parallel to each other.

Answer:

The image will be congruent to ΔMNP, 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.