Math, asked by sp941443pdnbe4, 1 year ago

diagonals AC and BD of a quadrilateral ABCD inresect at O in such a way that ar(AOD) =ar(BOC). Prove that ABCD is a trapezium

Answers

Answered by sonabrainly
2

Given -

a quad. ABCD ,

ar( AOD ) = ar ( BOC ).


To prove- ABCD is a trapezium


Proof -

ar(ADC)= ar ( AOD ) +ar(DOC)

similarly

ar(BDC) = ar(BOC) + ar(DOC)



ar( AOD ) = ar ( BOC ).

DOC IS COMMON HERE

Therefore,ar(ADC) = ar(BDC)

These two triangles are on the same base DC and their areas are also equal .

Therefore, they lie between the same parallels AB and DC.

AB||DC

Therefore, ABCD is a parallelogram with one pair of opposite sides parallel.

Therefore, ABCD is a trapezium.

mark as brainliest plz





Similar questions