How Many Diagonals in a Square

Edited By Team Careers360 | Updated on Aug 21, 2023 02:17 PM IST

Introduction

A line segment that connects any two non-adjacent vertices forms a square's diagonal. A square has two diagonals that are equally long and cut at an angle. When a square's side length is known, the diagonal of the square can be calculated using the diagonal of square formula.

Diagonal of a Square

A square has two diagonals, which are created by connecting the square's opposing vertices. In order to relate the properties of the diagonals, we may consider a square which has the following properties.

A square has identically long diagonals.
They are each other's perpendicular bisectors.
Two congruent isosceles and right-angled triangles are formed by dividing the square.

Diagonal of Square Formula

The diagonal of a square formula is d = a\sqrt{2} ; where d = the diagonal and a = the side of the square. The Pythagoras theorem is used to derive the formula for a square's diagonal.

Properties of diagonals of a square

Diagonals of a square are congruent: The two diagonals of a square have the same length, which is equal to the length of the side of the square. This means that the diagonals are congruent.

Diagonals of a square bisect each other: The diagonals of a square intersect at a point that is equidistant from the four vertices of the square. This means that the diagonals bisect each other at right angles.

Diagonals of a square form 45-degree angles: The diagonals of a square form 45-degree angles with each other and with the sides of the square. This is because the diagonals bisect each other at right angles, and the sides of a square are perpendicular to each other.

Diagonals of a square divide the square into two congruent right triangles: The two diagonals of a square divide the square into four congruent right triangles. Each right triangle has legs of equal length, which are half the length of the diagonal, and a hypotenuse of the same length as the side of the square.