Question

is △abc congruent to △def?
no △abc is not congruent to △def. you can not map △abc onto △def using rigid transformations
no △abc is not congruent to △def because the triangles have different orientations
yes △abc is congruent to △def. △abc was reflected over the line y = -3, then translated 3 units to the left and 1 unit down to get to △def
yes △abc is congruent to △def. △abc was reflected over the line y = -3, then translated 3 units to the right and 1 unit up to get to △def

Explanation:

Step1: Analyze rigid transformations

Rigid transformations (reflections, translations, rotations) preserve congruence.

Step2: Check the transformation description

If \(\triangle ABC\) is reflected over the line \(y = - 3\) (a reflection, which is a rigid transformation) and then translated (another rigid transformation). Rigid transformations do not change the shape and size of the triangle. So \(\triangle ABC\) and \(\triangle DEF\) are congruent.

Answer:

Yes \(\triangle ABC\) is congruent to \(\triangle DEF\). \(\triangle ABC\) was reflected over the line \(y=-3\), then translated 3 units to the left and 1 unit down to get to \(\triangle DEF\)