Question

ABC was constructed using triangle ABC and line segment EH. For EH to be the line of reflection between triangle ABC and triangle ABC, WHICH STATEMENT MUST BE TRUE?

A. EH should be the perpendicular bisector of segment BC.
B. EH should be an angle bisector of angle BAC.
C. EH should be an altitude of triangle ABC.
D. EH should coincide with one of the sides of triangle ABC.

Answer 1

Statement A must be true for EH to be the line of reflection between triangle ABC and triangle A'B'C'; EH must be the perpendicular bisector of segment BC.

Step-by-step explanation:

The question asks which condition must be true for EH to be the line of reflection between triangle ABC and triangle A'B'C'. Reflecting a shape across a line means that the line is equidistant from corresponding points on the shapes, hence behaving like a mirror. The correct statement is A. EH should be the perpendicular bisector of segment BC.

This is because for line EH to be the line of reflection, every point on triangle ABC must have a corresponding point on triangle A'B'C' that is the same distance from line EH but in the opposite direction. To satisfy this, EH must be equidistant from both B and C, and it must bisect segment BC at a 90-degree angle to ensure symmetry. Therefore, EH being the perpendicular bisector of BC is the necessary condition to confirm that triangles ABC and A'B'C' are mirror images over line EH.