Question

in this figure ABC &ABD are two triangles on the same base AB . If line segment CD is bisected by AB at O show that ar(ABC)=at(ABD).

Answer 1

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Answer 2

GIVEN:-

∆ABC and ∆ABD are two ∆s on the same base AB and AB bisects CD at a point O.

TO PROVE:-

$\small\sf{A(∆ABC)=A(∆ABD)}$

PROOF:-

$\small\sf{In\:∆ACD,AD\:is\:the\:median}$

$\small\sf{So,A(∆AOC)=A(∆AOD)}$.....(1)

$\large\sf{Now,In\:∆BCD,}$

$\small\sf{OB\:is\:the\:median}$

$\small\sf{So,A(∆BOC)=A(∆BOD)}$.....(2)

$\large\sf{Adding\:(1)\:and\:(2)}$

$\small\sf{A(∆AOC)+A(∆AOD)=A(∆BOC)+A(∆BOD)}$

$\therefore$$\small\sf{A(∆ABC)=A(∆ABD)}$