Which of the following transformations results in a shape that is congruent to…

Concept: Two shapes are congruent only when one can be produced from the other by a rigid transformation (isometry) — a transformation that preserves every distance and angle, keeping size and shape exactly the same. Reflection, translation, and rotation are rigid transformations; scaling, dilation, and shearing are not, since they change lengths or angles.

• Scaling by a factor of 2 multiplies every length by 2, enlarging the figure — similar to the original but not equal in size, so it is not congruent.

• Reflection flips the figure across a line without changing any length or angle, so the mirror image matches the original exactly in size and shape — it is congruent.

• Shearing displaces points parallel to a fixed direction by an amount proportional to their distance from it, which changes the angles between edges and distorts the figure — not congruent.

• Dilation resizes the figure from a center point by a scale factor, changing every length proportionally, the same way scaling does — similar but not congruent.

Cross-check: of the four transformations, only reflection preserves both length and angle at every point, confirming it produces the congruent shape.