Determine if the two figures are congruent and explain your answer.

Answer with explanation:

Two geometrical figures are said to be congruent , if their corresponding sides are equal and Corresponding interior angles are equal.

In Quadrilateral A B CD

  Using Distance formula to find distance between two points (a,b) and (c,d) and length of sides of Quadrilateral

In Quadrilateral E F G H

Comparing the corresponding sides

AB=EF=√5

BC=FG=√5

CD=GH=√17

DA=HE=√17

The corresponding sides are equal.So, the two geometrical shapes , that is Quadrilateral ABCD and Quadrilateral EFGH are congruent.

If you had patty paper (or something transparent) you could put it over one of the figures and match the shape, then flip it over 180 then translate it to the right until it was mapped on top of the other. (From CBAD perspective).

Since I can't, we will do something else.

We will map the coordinates and see if they are congruent:

F(1, -2)

E(3, -1)

H(4, -5)

G(0, -4)

Now for the other (same order)

B(-3, 2)

A(-1, 1)

D(0, 5)

C(-4, 4)

It's all set up. Now reflect FEHG over the x axis and translate it left to see if they match. From the looks of these coordinates, they do not. (sorry I'm in a rush)

Hope it was somewhat helpful, bye!

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step-by-step explanation:

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