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If medians of a triangle ABC intersects at G show that

ar (AGB) = ar (AGC) = ar(BGC) = ar (ABC).

Asked by Topperlearning User 4th June 2014, 1:23 PM
Answered by Expert
Answer:

In ABC, AD is the median

Ar(ABD) = ar(ACD) ...(i)

In GBC, GD is the median

(GBD) =ar(GCD) ...(ii)

Subtracting equation (ii) from equation (i)

Ar(ABD) - ar(GBD) = ar(ACD) - ar(GCD)

Ar(AGB) = ar(AGC)

Similarly, arAGB = ar(BGC)

arABC = arAGB + arBGC + arAGB

= arAGB + arAGB + arAGB

= 3 arAGB

ar ABC = ar(AGB)

Answered by Expert 4th June 2014, 3:23 PM
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