Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • The medians BE and CF of a triangle ABC intersect at G. Prove that the area of GBC = area of the quadrilateral AFGE.

The medians BE and CF of a triangle ABC intersect at G . Prove that the area of $\triangle G B C=$ area of the quadrilateral AFGE.

Answers (1)

Solution.

Given that the medians BE and CF of a triangle ABC intersect at G 
We know that the median divides a triangle into two triangles of the same area.

$
\begin{aligned}
& \quad \operatorname{ar}(\triangle B E C)=\frac{1}{2} \operatorname{ar}(\triangle A B C) \\
& \text { So, } \\
& \text { And, } \operatorname{ar}(\triangle A C F)=\frac{1}{2} \operatorname{ar}(\triangle A B C) \\
& \text { from }(1) \text { and (2) } \\
& \operatorname{ar}(\triangle A C F)=\operatorname{ar}(\triangle B E C) \\
& \therefore \operatorname{ar}(\triangle B G C)=\operatorname{ar}(G F A E)
\end{aligned}
$

This can be written as:
Area of $\triangle G B C=$ area of the quadrilateral AFGE .

Hence proved

 

Posted by

infoexpert26

View full answer

Similar Questions

Latest Question