State True/False:

The $∆\mathrm{ABC}$ and $∆\mathrm{EBC}$ both have a common base BC, then the area of $∆\mathrm{ABC}$ is same the area of $∆\mathrm{EBC}$.

From the figure, it is clear that $∆\mathrm{ABC}$ and $∆\mathrm{EBC}$ both have a common base BC, but they do not lie between the same parallels.

So, their areas can’t be equal.

Hence, the given statement is False.