9 grade maths> ABCD is a quadrilateral with diagonals AC...

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

alekhya , 10 Years ago

Grade 9

2 Answers

Harsh Patodia

Last Activity: 10 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

Last Activity: 6 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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9 grade maths> ABCD is a quadrilateral with diagonals AC...

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

alekhya , 10 Years ago

Harsh Patodia

Palak

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