In this chapter we will prove that in a triangle, a median divides it into two triangle of equal area.

**Given:**

Given below is the triangle ABC in which AD is the median.

Also AN is the altitude of the triangle

**To Prove:**

Median AD divide the triangle into two equal parts.

i.e. Area (ABD) = Area (ADC)

**Proof:**

Consider triangle ABD.

Area (ABD) = 1/2 x BD x AN –> eq (1)

Now consider triangle ADC.

Area (ADC) = 1/2 x DC x AN – -> eq (2)

Since AD is the median of triangle, we can write;

BD = DC

So eq (2) can be written asl

Area (ADC) = 1/2 x BD x AN –> eq(3)

Comparing eq (1) and eq(3), we are getting the same values.

So we can write;

Area (ABD) = Area (ADC)

Hence, the median divides the triangle into two equal parts.