Let a, b, and c represent positive real numbers. Use the figure in which 
has vertices at A(0,0), B(a,0), C(a+b,c), and D(b,c) to prove the following theorem.“If the diagonals of a parallelogram are equal in length, then the parallelogram is a rectangle.”
What will be an ideal response?
and 
are equal in length, then 
. Applying the Distance Formula, 
so 
. Also, 
so that 
.If , then 
.
Squaring, we have 
.
By subtraction of like terms, 
. In turn, 
. Dividing by 4, 
,
But only if a = 0 or b = 0.
Because a cannot equal 0 (points A and B would coincide), it is necessary that 
.
If , then the vertices of the parallelogram become A(0,0), B(a,0), C(a,c), and D(0,c).
Becuase these vertices lead to the relationship 
, ABCD must be a rectangle.
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A. slope is - 
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C. slope is -39
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