Question

Parallelograms an equal bases and between the same parallels are equal in area

• A. False
• B. True

Answer 1

Let us draw two parallelogram $ABCD$ and $EFCD$ that have same base $CD$ and lie between same parallels $AF$ and $CD$

Now, we shall prove that the both the parallelogram has same area.
Since, the opposite sides of parallelogram are parallel. So, $AD||BC$ with transversal $AF$
$\Rightarrow \angle DAB=\angle CBF$......(i)
Similar way, $ED||FC$ with transversal $EF$
$\Rightarrow \angle AED=\angle BFC$.....(ii)
Consider, two triangles $\Delta ADE$ and $\Delta BCF$
$\angle DAE=\angle CBF$ ( from equation(i))
$\angle AED=\angle BFC$ (from equation(ii))
$AD=BC$ (opposite sides are equal)
Thus, by AAS congruency rule, we say that
$\Delta ADE\cong \Delta BCF$
Therefore, area of $\Delta ADE=$ area of $\Delta BCF$
Now consider Area of $ABCD$=Area of $\Delta ADE+$Area of $BCDE$
$=$Area of $\Delta BCF+$Area of $BCDE$
$=$Area of $EFCD$
Hence, the area's of both parallelograms $ABCD$ and $EFCD$ are equal.
Therefore, the given statement is true.
Hence, the correct option is B (True).