If the polygons are similar, you should be able to map one polygon on top of the other using transformations.
Congruent Explanation: See solution.
Practice makes perfect
Let's start by graphing △ ABC and △ DEF.
The figures look like they are the same size so likely, we will not have to perform any dilation to map one of the figures on top of the other. However, the triangles do have different orientations which means we might have to rotate on of them and then, likely, translate it to map it on to the other
Rotation
Given the shape of the triangles, we can safely say that AB and DE are corresponding sides. Since one of them has a vertical orientation and the other has a horizontal orientation, we can rotate one of them 90^(∘) and align their orientations. Let's rotate △ DEF by 90^(∘) about the origin which means the coordinates of the triangles vertices change in the following way.
preimage (a,b) → image (- b,a)
Let's perform this rule on the given vertices of △ DEF.
Point
(a,b)
(- b,a)
D
(9,7)
(- 7,9)
E
(5,7)
(- 7,5)
F
(- 1,3)
(- 3,- 1)
Now we can draw D'E'F'.
Translation
Now the triangles have the same orientation but they are not mapped onto each other just yet. Looking at the vertices, we see that F' and C are corresponding vertices. If we translate △ D'E'F' by 1 unit to the right and 3 units down, we can map F' to C.
As we can see, △ D''E''F'' maps onto △ ABC. Since we were able to map one onto the other using only rigid motions, the shapes are congruent.
