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ABCD is a quadrilateral with diagonals AC and BD intersecting at O. If ar(DOC) = ar(AOB), show that :- angle BDA = angle DBC.

ABCD is a quadrilateral with diagonals AC and BD intersecting at O. If ar(DOC) = ar(AOB), show that :-     angle BDA = angle DBC.

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Grade:9

2 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
9 years ago
ar(DOC) = ar(AOB)
addind Ar(BOC to both sides.
we get
Ar (BDC)= Ar(ACB)
BUt they are on same base
This means AD || BC
angle BDA = angle DBC (alt interior angles)
Palak
15 Points
5 years ago
Given: ABCD is a quadrilateral in which diagonal AC and BD intersect at O , and ar(AOB) = ar(DOC) 
To prove : angle BDA = angle DBC
Proof : ar(AOB) =ar(DOC)
Adding ar(BOC) to both side 
ar(ACB)=ar(DBC)
We know triangles having same base and equal areas lies between same paralles
Therefore, AD|| BC
Now angle BDA = DBC ( alternate interior angle )
Hence proved 

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