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Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

Given => AD is the median,i.e,BD=DC andG is the M.P of AD to prove=> Ar. of tri.ABC=4 BGD PROOF Ar. of ABD=1/2 Ar. of tri. ABC [by mid point theorem] now,as G is the M.P of side AD of tri.ABD, BG is the median so, Ar. of tri.BGD= 1/2 Ar. ofADB It's proved before that Ar.of ADB is 1/2 Ar.ABC so, Ar.of bgd=1/2*[1/2 Ar. of ABC]= 1/4 Ar.of ABC in other words, Ar.of ABC= 4 Ar.of BGD HENCE THE PROOF :)

Given = AD is the median of Δ ABC. To prove = ar BGD = ar 4 ABC PROOF =So , ar ( Δ BAD ) = ar (Δ ADC) ( a median divides a triangle into two triangles of equal areas) - 1

As, G is the midpoint of AD... so BG is the median. so, ar (ΔBGD) = ar (Δ BGA) ( a median divides a triangle into two triangles of equal areas) -2

and, CG is also the median because it is joining the mid point of AD i,e G

ar (Δ DGC) = ar (ΔAGC) ( a median divides a triangle into two triangles of equal areas) -3