Question

is there a rigid transformation that would map δabc to δdec? yes, a reflection across side ac yes, a rotation about point c yes, a vertical translation no, triangles are not congruent

Explanation:

To determine the rigid transformation mapping \( \triangle ABC \) to \( \triangle DEC \), we analyze the triangles:

• \( \angle ACB \) and \( \angle DCE \) are vertical angles (or right angles, given the diagram), and sides \( AC = DC \), \( BC = EC \) (marked congruent).
• A rotation about point \( C \) (e.g., 180° or a rotation to align the triangles) would map \( \triangle ABC \) to \( \triangle DEC \) since rigid transformations preserve congruence, and the triangles share vertex \( C \) with corresponding sides/angles.
• A reflection across \( AC \) would not align \( B \) to \( E \) as needed. A vertical translation would not work because the triangles are not aligned vertically in a translational way. The triangles are congruent (by SAS, as \( \angle ACB=\angle DCE \), \( AC = DC \), \( BC = EC \)), so "no" is incorrect.

Answer:

yes, a rotation about point C