Properties of Kite

Various properties of the kite are added below,

• Kite has 2 diagonals that intersect each other at right angles.
• A kite is symmetrical about its main diagonal.
• Angles opposite to the main diagonal are equal.
• The kite can be viewed as a pair of congruent triangles with a common base.
• The shorter diagonal divides the kite into 2 isosceles triangles.
• The area of the kite is 1/2 × d₁ × d₂

Theorem: Diagonals of Kite Intersect at Right Angles

The interesting properties of the kite is that its diagonal are always perpendicular to each other. This is proved below, we have a kite ABCD, whose diagonal intersect each other at point O.

In ∆ABD and ∆BCD

AB = BC (Property of Kite)

AD = CD (Property of Kite)

BD = BD (Common Side)

Thus, ∆ABD ≅ ∆BCD (SSS congruency)

Now, in ∆ABC and ∆ADC

AB = BC (Property of Kite)

Hence  ∆ABC is an isosceles triangle.

AD = CD (Property of Kite)

Hence ∆ADC is an isosceles triangle.

∠BAO = ∠BCO

BO = BO (Common Side)

Thus, ∆ABO ≅ ∆BCO (SAS rule of congruency)

Now we know ∠AOB = ∠BOC

Also, ∠AOB + ∠BOC = 180° (Linear Pair)

Hence, ∠AOB = ∠BOC = 90°

Hence diagonals of kite intersect at right angles.

Kite is a special type of quadrilateral that is easily recognizable by its unique shape, resembling the traditional toy flown on a string. In geometry, a kite has two pairs of adjacent sides that are of equal length. This distinctive feature sets it apart from other quadrilaterals like squares, rectangles, and parallelograms.

Diagonals of kite intersect each other at right angles. It is one of the unique quadrilateral and has some interesting properties that are covered below in the article. In this article, we will learn about, Kite Quadrilateral, Properties of kites, Examples, and others, in detail.