CBSE Class 9 Answered
If medians of a triangle ABC intersects at
G show that
ar (AGB) = ar (AGC) = ar(BGC) = ar (ABC).
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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 | 04 Jun, 2014, 03:23: PM
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