Question

ABCD is a parallelogram whose diagonals intersect each other at O . Through O line segment PQ is drawn .Show that Op= OQ

Answer 1

Diagonals of a //gm bisect each other.
so ,
AO= OC
BO= DO
<AOD=< BOC
So, triangle AOD ~ triangle BOC.

NOW, PO = h of triangle AOD
OQ = h of triangle BOC

SO, PO = OQ ............ (h of congruent triangles)

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