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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