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: (ii) ar (DCB) = ar (ACB)

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:

(ii) $\small ar(DCB)=ar(ACB)$

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

Views

$ar(\Delta DOC)=ar(\Delta AOB)$
Now, add $ar(\Delta BOC)$ on both sides we get
$\\ar(\Delta DOC)+ar(\Delta BOC)=ar(\Delta AOB)+ar(\Delta BOC)\\ ar(\Delta DCB) = ar (\Delta ACB)$