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Areas of Parallelograms and Triangles
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15/07/2021 1:08 pm
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In Figure, E is any point on median AD of a ΔABC. Show that ar (ABE) = ar(ACE).
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15/07/2021 1:09 pm
Given,
AD is median of ΔABC.
∴ it will divide ΔABC into two triangles of equal area.
∴ ar(ABD) = ar(ACD) — (i)
ED is the median of ΔABC.
∴ ar(EBD) = ar(ECD) — (ii)
Subtracting (ii) from (i)
ar(ABD) – ar(EBD) = ar(ACD) – ar(ECD)
⇒ ar(ABE) = ar(ACE)