Question

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.​

Answer 1

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......