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.

Conclusion

In cases where the square's two diagonals are congruent, it is evident that the square has two diagonals. In a square, the diagonals are bisected.