Question

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: Analyze reflection across AC

A reflection across side AC would not map △ABC to △DEC as the orientation and position of vertices won't match.

Step2: Check rotation about C

By rotating △ABC about point C, we can align it with △DEC as the right - angle and the other angles and side - length relationships allow for such a rigid transformation. The right - angle at C in both triangles and the proportion of the sides can be matched through a rotation.

Step3: Evaluate vertical translation

A vertical translation will not map △ABC to △DEC as it only moves the triangle up or down and does not change the orientation to match the two triangles.

Step4: Determine congruency

The triangles appear to be congruent as they have equal angles (right - angles at C and another pair of equal angles as shown) and can be mapped onto each other by a rotation.

Answer:

yes, a rotation about point C