Q

# In Fig. 9.25, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that: (iii) DA || CB or ABCD is a parallelogram.

Q : 6     In Fig. $\small 9.25$, diagonals AC and BD of quadrilateral ABCD intersect at O such that $\small OB=OD$. If $\small AB=CD$, then show that:

(iii) $\small DA\parallel CB$ or ABCD is a parallelogram.

[Hint : From D and B, draw perpendiculars to AC.]

Views

Since $\Delta$DCB and $\Delta$ACB both lie on the same base BC and having equal areas.
Therefore, They lie between the same parallels BC and AD
$\Rightarrow$ CB || AD
also $\angle$1 = $\angle$2 [ already proved]
So, AB ||  CD
Hence ABCD is a || gm

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