Question

A figure is said to be regular if its sides are equal in length and angles are equal in measure. Can you identify the regular quadrilateral?

Answer 1

Hint: We use the given definition of a regular figure and use the properties of a regular figure to identify the quadrilateral having these properties. Write different types of quadrilateral and choose the one having properties of all sides of equal length and all angles of equal measure.

Complete answer:
We are given that a figure is said to be regular if its sides are equal in length and angles are equal in measure.
We have to find which quadrilateral is a regular quadrilateral.
We know a quadrilateral is a closed figure having four vertices (corners) and four edges (sides). There are many types of quadrilateral. Some of them are Square, Rectangle and Trapezium etc. We define some of these well-known quadrilaterals and check which satisfies the properties for a regular quadrilateral i.e. which of them has all sides equal and all angles of equal measure.
Rectangle: A rectangle is a quadrilateral having all angles as right angles and opposite sides equal and parallel to each other.
\[ \Rightarrow \]A rectangle is not regular as all sides are not equal.
Trapezium: A quadrilateral having one pair of opposite sides parallel is called a trapezium.
Since other pair of sides is not parallel to each other, then trapezium is not a kind of parallelogram
\[ \Rightarrow \]A trapezium is not regular as all sides are not equal.
Square: A square is a quadrilateral with all sides of equal length, all angles as right angles and opposite sides parallel to each other.
\[ \Rightarrow \]A square is regular as all sides are equal and all angles are also equal in measure.
Rhombus: A rhombus is a quadrilateral whose all sides are of equal length and opposite sides are parallel to each other. Opposite angles of rhombus are equal in measure.
\[ \Rightarrow \]A rhombus is not regular as all angles are not equal.
\[\therefore \] Square is a regular quadrilateral

Note:
Many students make the mistake of writing polygons with different numbers of sides as types of quadrilaterals, keep in mind polygons are figures with different numbers of sides and quadrilaterals are figures only with four numbers of sides.