Manipur Board Solutions for Chapter: Quadrilaterals, Exercise 1: EXERCISE 8.1

In a $∆ABC$, median $AD$ is produced to $E$ such that, $AD=DE$. Prove that $ABEC$ is a parallelogram.

$ABCD$ is a rectangle in which diagonal $AC$ bisects $\angle A$ as well as $\angle C$. Show that diagonal $BD$ bisects $\angle B$ and $\angle D$.

$ABCD$ is a parallelogram. $P$ and $Q$ are points on $AB$ and $DC$ respectively such that $AP=CQ$. Prove that $PQ$ and $BD$ bisect each other.

$ABCD$ is a parallelogram. The side $AB$ is produced to $E$ such that $AB=BE$. Prove that $ED$ bisects $BC$.

$ABC$ and $DEF$ are two triangles such that $AB$ and $BC$ are respectively equal and parallel to $DE$ and $EF$. Vertices $A, B$ and $C$ are joined to vertices $D, E$ and $F$ respectively. Show that $ABED$ is a parallelogram.

$ABC$ and $DEF$ are two triangles such that $AB$ and $BC$ are respectively equal and parallel to $DE$ and $EF$. Vertices $A, B$ and $C$ are joined to vertices $D, E$ and $F$ respectively. Show that $BEFC$ is a parallelogram.

$ABC$ and $DEF$ are two triangles such that $AB$ and $BC$ are respectively equal and parallel to $DE$ and $EF$. Vertices $A, B$ and $C$ are joined to vertices $D, E$ and $F$ respectively. Show that $ACFD$ is a parallelogram.

$ABC$ and $DEF$ are two triangles such that $AB$ and $BC$ are respectively equal and parallel to $DE$ and $EF$. Vertices $A, B$ and $C$ are joined to vertices $D, E$ and  respectively. Show that $∆ABC\cong ∆DEF$