Question 1040566
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<pre><b>
There are four methods to show it:

1.  A parallelogram is a quadrilateral with both pairs of 
opposite sides parallel. 

A. Use the slope formula to show that AB is parallel to CD
B. Use the slope formula to show that BC is parallel to AD


2,  If both pairs of opposite sides of a quadrilateral are 
congruent, the quadrilateral is a parallelogram. 

A. Use the distance formula to show that AB and CD have the 
same length and therefore are congruent.
B. Use the distance formula to show that BC and AD have the 
same length and therefore are congruent.

3.  If the diagonals of a quadrilateral bisect each other, 
the quadrilateral is a parallelogram. 

A. Use the midpoint formula to find the midpoint of diagonal AC.
B. Use the midpoint formula to find the midpoint of diagonal BD 
to show that the two midpoints are the same.

4.  If ONE PAIR of opposite sides of a quadrilateral are BOTH 
parallel and congruent, the quadrilateral is a parallelogram.

If you have done both 1 and 2, you have already done enough to 
show that AD and BC are both parallel and congruent.

If you have trouble, tell me in the thank-you note form below and
I'll get back to you by email.

Edwin</pre></b>