Question

How many things do we need to know to construct a quadrilateral?

Answer 1

Define a quadrilateral and enlist the parameters for constructing a quadrilateral

A quadrilateral is defined as a closed figure with four sides and four angles.

There are in total $10$ parameters which are useful in the construction of a quadrilateral

Four sides, four angles and two diagonals.

$5$ parameters out of $10$ are required to construct a quadrilateral

For example: Construct a quadrilateral ABCD in which $AB=5cm$,$\angle ABC={60}^{\circ }$, $\angle BAD={80}^{\circ },BC=3cm,AD=2cm$

1. Draw $AB=5cm$
2. From vertex $B$ draw a ray making an angle of ${60}^{\circ }$with $AB$
3. With $B$ as center and radius equal to $3cm$ draw an arc on the ray at $C$
4. From vertex $A$ draw a ray making an angle of ${80}^{\circ }$ with $AB$
5. With $A$ as center and radius equal to $2cm$ draw an arc on the ray at $D$
6. Join $CD$

Hence, a quadrilateral can be constructed with $5$ given parameters out of the $10$ parameters in a quadrilateral.