SOLUTION: Quadrilateral ABCD has vertices A(0,-2), B(9,1), C(4,6), and D(1,5). Prove: a) Quadrilateral ABCD is a trapezoid. b) Quadrilateral ABCD is an isosceles trapezoid.

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Question 119374: Quadrilateral ABCD has vertices A(0,-2), B(9,1), C(4,6), and D(1,5). Prove: a) Quadrilateral ABCD is a trapezoid. b) Quadrilateral ABCD is an isosceles trapezoid.
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
Quadrilateral ABCD has vertices A(0,-2), B(9,1), C(4,6), and D(1,5). Prove: a) Quadrilateral ABCD is a trapezoid. b) Quadrilateral ABCD is an isosceles trapezoid. 



First we prove that AB and DC are parallel, 
by showing they have the same slope:

Slope of AB
     
m =  =  =  = 

Slope of DC

m =  = 

There are both  so they are parallel and so ABCD is
a trapezoid.

To show that it is isosceles, we prove that AD = CB

Length of AD

d =  =  =  = 
=  =  =  

Length of CB

Length of AD

d =  =  =  =  =  =  

These are both  so it is also isosceles.

Edwin
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