Prove that the diagonals of a parallelogram divide it into four triangle of equal are.

In the figure given below, $AD$ is the median of triangle  $ABC$ and $P$ is any point on $AD$. Prove that the area of the triangle $PBD=$ the area of triangle $PDC$.

In the figure given below, $AD$ is the median of triangle  $ABC$ and $P$ is any point on $AD$. Prove that the area of the triangle $ABP=$ the area of triangle $APC$.

In the figure given below, $DE\left|\right| BC$, prove that the area of the triangle $ACD=$ area of the triangle $ABE$. 

In the figure given below, $DE\left|\right| BC$, prove that the area of the triangle $OBD=$ area of the triangle $OCE$.

In the figure given below, $ABCD$ is parallelogram and $P$ is any point in $BC$. Prove that the area of triangle  $ABP +$ the area of triangle $DPC =$ area of triangle $APD$.

In the figure given below, $\mathrm{O}$ is any point inside a parallelogram $\mathrm{ABCD}$. Prove that area of $∆\mathrm{OAB}+$ area of $∆\mathrm{OCD}=\frac{1}{2}$ area of $\Vert \mathrm{gmABCD}$.

In the figure given below, $\mathrm{O}$ is any point inside a parallelogram $\mathrm{ABCD}$. Prove that area of $∆\mathrm{OBC}+$ area of $∆\mathrm{OAD}=\frac{1}{2}$ area of $\Vert \mathrm{gmABCD}$.