Answer: The triangles are not congruent because △D′E′F′ is a dilation of △DEF .
Step-by-step explanation:
Rigid motions form congruent figures, the common rigid motions are:
1) translation (moves figure about some distance)
2) reflection (creates mirror image)
3) rotation (rotate figure about some degrees)
Dilation : It does not create congruent images. It creates an image that is the exactly same shape as the original, but have a different size with the help of a scale factor k .
Given : The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.
Here the coordinates of the image are increased by using a scale factor 2.
So △D′E′F′ must be an enlargement of △DEF.
⇒△D′E′F′ is a dilation of △DEF
It means : The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.