In parallelogram

MATHEMATICS · Subjective · CBSE · Mathematics · Quadrilaterals · Quadrilaterals

Problem

In parallelogram

ABCD

, points

E

and

F

are the mid-points of sides

AB

and

CD

respectively. Diagonals

AC

and

BD

intersect at

O

. Lines

EO

and

FO

are drawn. (i) Prove that

\triangle AOE

and

\triangle COF

are congruent. (ii) Hence, show that

\text{area}(\triangle AOE) = \text{area}(\triangle COF)

. (iii) Prove that the area of quadrilateral

AOCF

is equal to the area of quadrilateral

BOED