Question

the triangles are congruent by the sss congruence theorem. which rigid transformation(s) can map △abc onto △dec? reflection, then rotation reflection, then translation rotation, then translation rotation, then dilation

Explanation:

Step1: Recall rigid - transformations

Rigid transformations include rotation, reflection, and translation. Dilation is not a rigid - transformation as it changes the size of the figure.

Step2: Analyze mapping of congruent triangles

Since \(\triangle ABC\) and \(\triangle DEC\) are congruent (by SSS), we need to use only rigid - transformations to map one onto the other. First, a reflection can be used to flip \(\triangle ABC\) to match the orientation of \(\triangle DEC\) in terms of side - to - side correspondence. Then, a translation can be used to move \(\triangle ABC\) so that it coincides with \(\triangle DEC\).

Answer:

reflection, then translation