Question

The diagonals of a parallelogram divide it into four triangles of equal area

• A. True
• B. False

Answer 1

The correct option is A True

Given:- $ABCD$ is a $//gm$.

To prove:-$\Delta AOB\cong \Delta BOC\cong \Delta COD\cong \Delta DOA$

Proof:- In $\Delta AOB$ & $\Delta COD$

$\angle BAO=\angle DCO$ (alternate interior angle)

$AB=CD$ (opp. sides are equal)

$\angle ABO=\angle CDO$ (alternate interior angle)

Therefore, $\Delta AOB\cong \Delta COD$ by $AAS$ Congruence criterion.

Similarly,

$\Delta AOB\cong \Delta BOC\cong \Delta COD\cong \Delta DOA$

Hence Digonals of parallelogram divides four triangle of equal area.