Question

Show that a median of a triangle divides it into two triangles of equal area....

Plz answer

Answer 1

Take a ∆ ABC with the mid point D on the side BC and height AE

BD = DC (As D is the midpoint ) --(1)

Now take a ∆ABD 

Area of ∆ ABD = ½ base × height

                                  = ½×BD ×AE --(2)

Now take a ∆ BDC

Area of ∆BDC = ½ ×base × height

                                  = ½ × DC ×AE --(3)

From --(1), --(2) and --(3)

 Area of ∆ ABD = Area of ∆DBC

Therefore a median divides a triangle into two triangles of equal area.

$\blue{Hence \:Proved}$

Answer 2

Take a ∆ ABC with the mid point D on the side BC and height AE

BD = DC (As D is the midpoint ) --(1)

Now take a ∆ABD

Area of ∆ ABD = ½ base × height

= ½×BD ×AE --(2)

Now take a ∆ BDC

Area of ∆BDC = ½ ×base × height

= ½ × DC ×AE --(3)

From --(1), --(2) and --(3)

Area of ∆ ABD = Area of ∆DBC

Therefore a median divides a triangle into two triangles of equal area.

\blue{Hence \:Proved}HenceProved