Question

In Figure, $E$ is any point on median $AD$ of a $△ABC$. Show that area$△ABE=$area$△ACE$.

Answer 1

Show that area$△ABE=$area$△ACE$:

Given: $AD$ is the median of $△ABC$.

So, It divides $△ABC$ into two equal-area triangles.

Now,

area$△ABD=$ area$△ACD\to \left(1\right)$

Also,

$ED$ is the median of $△EBC$.

Therefore,

area$△EBD=$ area$△ECD\to \left(2\right)$

On subtracting equation $\left(2\right)$ from $\left(1\right)$, we get

$\Rightarrow$ area$△ABD$ $-$ area$△EBD=$ area$△ACD-$ area$△ECD$

$\Rightarrow$ area$△ABE=$area$△ACE$

Hence proved that area$△ABE=$area$△ACE$..