Question

ABCD is a trapezium in which AB is parallel to DC. If diagonals AC and BD intersect at O, prove that
ar ( AOD)=ar(BOC)

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Answer 1

Answer:

Step-by-step explanation

ABD AND ABC ARE ON THE SAME BASE AND PARALLEL

AREA ABD =AREA ABC

SUBTRACT AOB ON BOTH SIDES

AR ABD - AR AOB = AR ABC - AR AOB

AR AOD =AR BOC

HENCE PROVED

Answer 2

$triangle \: abd \: = triangle \: abc(between \: same \: base \: ab \: and \: ab \: is \: parallel \: to \: dc \\ subtract \: triangle \: \: aob \: on \: both \: sides \\ trangle \: abd - triangle \: aob \: = triangle \: abc - triangle \: aob \\ triangle \: aod \: = triangle \: boc \\ hence \: area \: of \: triange \: aod \: = area \: of \: triangle \: boc \\ proved$