SOLUTION: Determine whether the polygons with the given vertices are similar. Quadrilateral ABCD with vertices A(�5, 4), B(�2, 4), C(�2, 2), D(�5, 2) and quadrilateral EFGH with vertices E

Question 945562: Determine whether the polygons with the given vertices are similar.
Quadrilateral ABCD with vertices A(�5, 4), B(�2, 4), C(�2, 2), D(�5, 2)
and quadrilateral EFGH with vertices E(�2, 0), F(4, 0), G(4, �6), H(�2, �6).
Can someone help me ? Thank you ! If any work please show the work, thanks so much.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
It is easier to see if you graph them:
and

But even without drawing them, you could figure it out:
ABCD is a rectangle because
AB is a horizontal line because the y-coordinate for both points (A and B) is the same: 4.
CD is a horizontal line because the y-coordinate for both points (C and D) is the same: 2.
BC is a vertical line because the x-coordinate for both points (B and C) is the same: -2.
AD is a vertical line because the x-coordinate for both points (A and D) is the same: -5.
Sides AB and CD have .
Sides AD and BC have .
So, ABCD is a rectangle whose sides are in the ratio 3:2.

To be similar, EFGH must be a rectangle,
and its side lengths must be in the same 3:2 ratio.
In the general meaning of the term rectangle, EFGH is a rectangle too, because
EF is a horizontal line because the y-coordinate for both points (E and F) is the same: 0.
GH is a horizontal line because the y-coordinate for both points (G and H) is the same: -6.
FG is a vertical line because the x-coordinate for both points (F and G) is the same: 4.
EH is a vertical line because the x-coordinate for both points (E and H) is the same: -2.
However,
sides EF and GH have , and
sides FG and EH have ,
So the side lengths are in a 1:1 ratio.
The rectangle EFGH is a square,
not at all similar to the rectangle ABCD.
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