show that the line segments joining the mid-points of the opposite sides of a quad bisect each other
Asked by ridhisood | 6th Jan, 2010, 07:05: PM
let ABCD be the quadrilateral.
P,Q,R,S be the mid ptsof AB,BC,CD,DA.
join diagonal AC.
Join S,R and P,Q.
in triangles DAC,
S and R are mid pts of sides, so,
SR II AC... and SR=1/2 (AC) ...Mid pt thm
PQ II AC and PQ=1/2?(AC)
PQRS is a parallelogram as one pair of opp sides is parallel an equal.(this can be proved even by taking the other diagonal and using the fact that when both pairs of opp sides are paralle, the quad is a parallelogram)
PR and SQ become the diagonals of the parallelogram PQRS, SO they must bisect each other.
Answered by | 7th Jan, 2010, 09:11: AM
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