K C Sisodia Solutions for Chapter: Geometry, Exercise 7: TEST YOUR SKILLS

$M and N$ points are taken on the diagonal $AC$ of a parallelogram $ABCD$ such that $AM=CN$. Prove that $BMDN$ is a parallelogram.

In the given figure, $AP$ is bisector of $\angle A$ and $CQ$ is bisector of $\angle C$ of parallelogram $ABCD$. Prove that $APCQ$ is a parallelogram.

$ABCD$ is a square. $A$ is joined to a point $P$ on $BC$ and $D$ is joined to a point $Q$ on $AB$. If $AP=DQ$; prove that $AP and DQ$ are perpendicular to each other.

In a $\square ABCD$, $AB=AD$ and $CB=CD$. Prove that $AC$ bisects $\angle BAD$.

In $\square ABCD$, $AB=AD$ and $CB=CD$, Prove that $AC$ is perpendicular bisector of $BD$.

In the given figure, $ABCD$ is a trapezium in which $DA\parallel CB$. $AB$ has been produced to $E$. Find the angles of the trapezium.

In a $\square ABCD$, $AB\parallel DC$ and $AD=BC$. Prove that $\angle A=\angle B$ and $\angle C=\angle D$.

In the figure given below, $ABCD$ is a rectangle and diagonals intersect at $O$. $AC$ is produced to $E$. If $\angle ECD=146°$, find the angles of $△AOB$.