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ICSE Class 9 Answered

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Asked by Kanwaranita10 | 30 Jan, 2019, 08:46: PM
answered-by-expert Expert Answer
Figure shows a triangle, G is the intersection point of medians.
 
we know, from the properties of median, G is centroid of triangle and   AF:GF = 3:1 .  Hence GF = (1/3)AF

Let us draw perpendicular lines  AD and GE to BC

ΔADF and Δ GEF are right angled triangle, begin mathsize 12px style angle end styleDAF = begin mathsize 12px style angle end styleEGF (alternate angles).
Hence ΔADF and Δ GEF are similar triangles. Hence GE = (1/3)AD ......................(1)
 
Area of triangle ABC = (1/2)×BC×AD .............................(2)
 
Area of triangle BCG = (1/2)×BC×GE .............................(3)
 
Using eqn.91) in (3), we write, Area of triangle BCG  = (1/2)×BC×(1/3)AD ...................(4)
 
By comparing eqn.(2) and (4),  we get,  Area of triangle BCG  = (1/3)Area of triangle ABC
Answered by Thiyagarajan K | 31 Jan, 2019, 10:18: AM

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