Question

In $△ABC$ , $E$ and $F$ are mid-points of sides $AB$ and $AC$ respectively. If $BF$ and $CE$ intersect each other at point $O$, then the $△OBC$ and quadrilateral $AEOF$ are equal in area.

• A. True
• B. False

Answer 1

The correct option is A True

Given that $E$ and $F$ are mid points. We have to prove that $a_1\left(BOC\right)=a_1\left(AEOF\right)$

As $EF\parallel BC$ (By midpoint theorem.)

$a_1\left(△BEF\right)=a_1\left(△ACFE\right)$ ($\because$ Between the parallel lines.)

$a_1\left(△BEF\right)-a_1\left(△EOF\right)=a_1\left(△CFE\right)-a_1\left(△EOF\right)\therefore a_1\left(△BOE\right)=a_1\left(△FOC\right)⟶\left(i\right)$

$a_1\left(AEOF\right)=a_1\left(BOC\right)$

$\therefore$ The statement is true.