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.