Unformatted text preview: + + + , x1 x22 x3 x422 + + + y1 y22 y3 y422 + + + , + + + Rx1 x2 x3 x44 y1 y2 y3 y44 Similarly, let S be the midpoint of NQ; then S has coordinates: + + + , x2 x32 x4 x122 + + + y2 y32 y4 y122 + + + , + + + Sx1 x2 x3 x44 y1 y2 y3 y44 It follows that points R and S coincide since they have the same coordinates. This means that segments MP and NQ have the same midpoint. But this is one of the characteristic properties of parallelograms: a quadrilateral is a parallelogram if and only if the diagonals bisect each other at a common point. Hence, this proves that MNPQ is a parallelogram....
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This note was uploaded on 07/22/2011 for the course ME 3 taught by Professor Prof.ramachandran during the Spring '11 term at Indian Institute of Technology, Kharagpur.
- Spring '11