Question

proving triangle congruence. is there a rigid transformation that would map △abc to △dec? yes, a reflection across side ac yes, a rotation about point c yes, a vertical translation no, triangles are not congruent

Explanation:

Step1: Recall rigid - transformation properties

Rigid transformations preserve shape and size. Types include reflection, rotation, and translation.

Step2: Analyze reflection across side AC

A reflection across side AC would map point A to itself, point C to itself, and if the triangles are symmetric about AC, point B would map to point E and point D would map to a corresponding point on the other side. Since we have right - angled triangles with equal sides (marked by congruence symbols), a reflection across side AC can map $\triangle ABC$ to $\triangle DEC$.

Step3: Analyze rotation about point C

A rotation about point C would change the orientation of the triangles in a way that they would not coincide.

Step4: Analyze vertical translation

A vertical translation would move the triangles up or down without rotating or reflecting them, and they would not coincide.

Step5: Check congruence

The triangles appear to be congruent based on the right - angle and the marked equal sides.

Answer:

yes, a reflection across side AC