Answer :
△DEF is congruent to △D'E'F' because you can map △DEF to △D'E'F' using a reflection across the x-axis, which is a rigid motion.
What does a math congruent mean?
Congruent refers to having precisely the same form and size. Even after the shapes have been flipped, turned, or rotated, the shape and size ought to remain constant.
1) Reflections, rotations and translations are rigid transformations, because they do not modify the lengths of the segments nor the angles, so the images and the preimages are congruents.
2) Let's see what transformation map △DEF is to △D'E'F' by analyzing the vertices of preimage and image:
Preimage Image
D (-3, -1) D' (-3, 1)
E (2, -4) E' (2, 4)
F (4, -4) F' (4, 4)
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