A square with side given can be constructed by using the property of its diagonals.

Can we construct a rhombus $ABCD$ with $AB=4\ cm$? Its diagonal intersect at the point $O$ and $\angle OAB = 60^0$.

We cannot construct a square if:

When given a square, the construction of an angle bisector at any vertex will create the diagonal of the square. 

You are given the length of a diagonal of a rhombus and one of the angles of the rhombus. Which property of the rhombus will be used in the construction of this rhombus?

If we have to construct a square $PQRS$ whose diagonal is $8 \sqrt 2$ cm then its side is equal to ?

State the following statement is True or False
The side of a square is $\sqrt2$ times the diagonal of a square

State the following statement is True or False
We cannot construct the square if only diagonal is given

Which of the following statements is true for a rhombus?

What would be the length of side $BC$ in Square $ABCD$ if the diagonal of the square given is $10$ cm?

If one diagonal of a square is the portion of the line $\frac { x }{ a } +\frac { y }{ b } =1$ intercepted by the axes, then the extremities of the other diagonal of the square are

The side of a regular hexagon is 'p' cm then its area is

The diagonal of rectangle $ABCD$ intersect each other at $O$. If $\angle AOB = 30^0$, then we can construct a rectangle if _________ is given.

We can construct a parallelogram if:

Construct a parallelogram $ABCD$ with $AB=24$ cm and $AD=16$ cm. The distance between AB and DC is $10$ cm. Find the area of parallelogram $ABCD$ in sq. cm.

Construct a parallelogram $ABCD$, with adjacent sides $AB=4$ cm, $BC = 5$ cm and height corresponding to  (base) $BC = 3.5$ cm. Find the area of parallelogram ABCD in sq. cm.

State whether the following statement is True or False.
The length of diagonal of rectangle is more than any side of rectangle.

Construct a rectangle $ABCD$, where $AB=10$ cm and $BC=8$ cm.Steps for its construction is given in a jumbled form. Identify its correct sequence.
1) Join these cuts with a line $CD$ and rectangle $ABCD$ is formed
2) Draw a straight line $AB$ of length $10$ cm
3) Draw perpendicular lines at $A$ and $B$ using protractor.
4) Using compass cut arc at the perpendicular from $A$ and $B$ of lengths $8$ cm

Let $ABCD$ be a square in which $A$ lies on the positive y-axis and $B$ lies on the positive x-axis. If $D$ is the point $(12, 17)$ the coordinates of $C$ are.

Construct a parallelogram $ABCD$ with $AB=24$ cm and $AD=16$ cm. The distance between AB and DC is $10$ cm. Find the distance between AD and BC.