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Areas of Parallelograms and Triangles
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16/07/2021 3:55 pm
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In Figure, ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, show that: ar(ABC) = ar(ABD).
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16/07/2021 3:58 pm
In ΔABC, AO is the median. (CD is bisected by AB at O)
∴ ar(AOC) = ar(AOD) — (i)
ΔBCD, BO is the median. (CD is bisected by AB at O)
∴ ar(BOC) = ar(BOD) — (ii)
Adding (i) and (ii)
We get,
ar(AOC) + ar(BOC) = ar(AOD) + ar(BOD)
⇒ ar(ABC) = ar(ABD)