Question

The median of any triangle bisects it into two triangles of equal areas.

• A. True
• B. False

Answer 1

The correct option is A

True

Consider the figure:

The median $AD$ bisects $△ABC$ into two triangles $△ABD$ and $△ACD$.

We have to check whether area of $△ABD=$ area of $△ACD$.

To check that, draw $AE\perp BC$

Now, area of $△ABD=\frac{1}{2}\times BD\times AE$ ... (i)

area of $△ACD=\frac{1}{2}\times CD\times AE$ ... (ii)

Since, $AD$ is the median, so, $BD=CD$

$\Rightarrow$ Eq. (i) $=$ Eq. (ii)

$\Rightarrow$ area of $△ABD=$ area of $△ACD$

Thus, the given statement is true.