In this chapter we will prove that in a triangle, a median divides it into two triangle of equal area.
Given below is the triangle ABC in which AD is the median.
Also AN is the altitude of the triangle
Median AD divide the triangle into two equal parts.
i.e. Area (ABD) = Area (ADC)
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.