Question

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

Explanation:

Step1: Analyze rigid transformations

Rigid transformations include reflection, rotation, and translation. Dilation is not a rigid transformation as it changes the size of the figure. So we can eliminate the option with dilation.

Step2: Consider the orientation

If we first rotate \(\triangle ABC\) around point \(C\) to align the sides and then translate it (move it without rotation or reflection) to map it onto \(\triangle DEC\). Reflection would change the orientation in a way that is not needed here.

Answer:

rotation, then translation