Question

triangle abc is congruent to △abc by the hl theorem. what single rigid transformation maps △abc onto △abc? options: dilation, reflection, rotation, translation

Explanation:

To determine the rigid transformation, we analyze each option:

• Dilation: Changes size, not rigid (eliminated).
• Reflection: Flips over a line (the line through \( B \) perpendicular to \( AC \) and \( A'C' \) would map \( \triangle ABC \) to \( \triangle A'BC' \), as the triangles are mirror images over this line).
• Rotation: Requires a center and angle, but the triangles are symmetric over a vertical line through \( B \), not rotated.
• Translation: Shifts without rotation/reflection, but the triangles are mirrored, not shifted.

Thus, reflection is the correct rigid transformation.

Answer:

B. reflection