M L Aggarwal Solutions for Chapter: Quadrilaterals, Exercise 1: Exercise 8.1

All the four sides of a quadrilateral are equal. What special name can be given to this quadrilateral?

Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer.

Diagonals of a rectangle are equal and perpendicular. Is this statement true? Give reason for your answer.

Diagonals of a rhombus are equal and perpendicular to each other. Is this statement true? Give reason for your answer.

Diagonals $AC$ and $BD$ of a quadrilateral intersect each other at $O$ such that $OA:OC=3:2$. Is $ABCD$ a parallelogram? Why or why not?

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Diagonals of a rhombus are of lengths $16 \mathrm{cm}$ and $12 \mathrm{cm}$ respectively, find the perimeter of the rhombus.

In the following figure, through $A, B$ and $C$, lines $RQ, PR$ and $QP$ have been drawn respectively parallel to sides $BC, CA$ and $\mathrm{AB}$ of a triangle $\mathrm{ABC}$. Show that $\mathrm{BC}=\frac{1}{2}\mathrm{RQ}$.