Question

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

Explanation:

Step1: Analyze rigid transformations

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

Step2: Consider reflection and translation

If we first reflect \(\triangle ABC\) over an appropriate line (to get the orientation closer) and then translate (to move it to the exact position of \(\triangle DEC\)), we can map \(\triangle ABC\) onto \(\triangle DEC\). Rotation - then - translation won't work as the orientation after rotation is not correct for a simple translation. Reflection - then - rotation is more complex than needed.

Answer:

reflection, then translation