In a parallelogram ABCD, the diagonals AC and BD interest each other at O through , a line is drawn to intersect AD at X and BC at Y . show that OX=OY.
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Step-by-step explanation:
To prove OX=OY
Proof- As we know that the diagonal of parallelogram bisect each other
We have,
In traingle COY and triangle AOX
CO=AO (diagonals bisects each other at)
angle 1 =angle 2. (by vertical angles)
angle 3= angle 4. (alternate interior angles)
triangle COY is (congruent) to triangle AOX (by ASA)
Hence,OX=OY, Proved......
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