Properties of Kite

A kite shape is a quadrilateral that has 2 pairs of equal adjacent sides. Another important feature of a kite shape is that the diagonals of a kite always intersect at 90°. Let us learn more about the properties of a kite shape.

A kite shape is a quadrilateral in which two pairs of adjacent sides are of equal length. No pair of sides in a kite are parallel but one pair of opposite angles are equal.

A kite is a quadrilateral that has two pairs of consecutive equal sides and perpendicular diagonals. The longer diagonal of a kite bisects the shorter one. Observe the following kite ACBD to relate to its properties given below.

We can identify and distinguish a kite with the help of the following properties:

• A kite has two pairs of adjacent equal sides. Here, AC = BC and AD = BD.
• It has one pair of opposite angles (obtuse) that are equal. Here, ∠A = ∠B
• In the diagonal AB, AO = OB.
• The shorter diagonal forms two isosceles triangles. Here, diagonal 'AB' forms two isosceles triangles: ∆ACB and ∆ADB. The sides AC and BC are equal and AD and BD are equal which form the two isosceles triangles.
• The longer diagonal forms two congruent triangles. Here, diagonal 'CD' forms two congruent triangles - ∆CAD and ∆CBD by SSS criteria. This is because the lengths of three sides of ∆CAD are equal to the lengths of three sides of ∆CBD.
• The diagonals are perpendicular to each other. Here, AB ⊥ CD.
• The longer diagonal bisects the shorter diagonal.
• The longer diagonal bisects the pair of opposite angles. Here, ∠ACD = ∠DCB, and ∠ADC = ∠CDB
• The area of a kite is half the product of its diagonals. (Area = 1/2 × diagonal 1 × diagonal 2).
• The perimeter of a kite is equal to the sum of the length of all of its sides.
• The sum of the interior angles of a kite is equal to 360°.

Angles in a Kite

As discussed in the properties of a kite, we know that a kite has 4 interior angles. Here are the features of the angles of a kite.

• The 4 interior angles of a kite always sum up to 360° as in the case of every quadrilateral.
• One pair of non-adjacent angles (the obtuse angles) are equal.

As we have discussed in the earlier section, a kite has 2 diagonals. The important properties of the diagonals of a kite are given below.

• The two diagonals are not of the same length.
• The diagonals of a kite intersect each other at right angles. It can be observed that the longer diagonal bisects the shorter diagonal.
• A pair of diagonally opposite angles of a kite are said to be congruent.
• The shorter diagonal of a kite forms two isosceles triangles. This is because an isosceles triangle has two congruent sides, and a kite has two pairs of adjacent congruent sides.
• The longer diagonal of a kite forms two congruent triangles by the SSS property of congruence. This is because the three sides of one triangle to the left of the longer diagonal are congruent to the sides of the triangle to the right of the longer diagonal.

Challenging Questions

• Can a kite be called a parallelogram?
• Can a kite have sides of 12 units, 25 units, 13 units, and 25 units?

Important Notes

Some important points about a kite are given below.

• A kite is a quadrilateral.
• A kite satisfies all the properties of a cyclic quadrilateral.
• The area of a kite is half the product of its diagonals.

☛Related Articles

• Measurement
• Area of a Kite
• Types of Quadrilaterals
• Congruence in Triangles
• SSS Formula

What is a Kite in Geometry?

In Geometry, a kite is a quadrilateral in which 2 pairs of adjacent sides are equal. It is a shape in which the diagonals intersect each other at right angles.

What is the Shape of a Kite?

The shape of a kite is a unique one that does not look like a parallelogram or a rectangle because none of its sides are parallel to each other. It is symmetrical in shape and can be imagined as the real kite which is used for flying.

How to Find the Area of a Kite?

The area of a kite is the space occupied by it. It can be calculated using the formula, Area of kite = 1/2 × diagonal 1 × diagonal 2. For example, if the lengths of the diagonals of a kite are given as 7 units and 4 units respectively, we can find its area. After substituting the values in the formula, we get, Area of kite = 1/2 × 7 × 4 = 14 unit²

What are the Angles of a Kite Shape?

A kite has 4 interior angles and the sum of these interior angles is 360°. In these angles, it has one pair of opposite angles that are obtuse angles and are equal.

What are the Properties of a Kite Shape?

A kite is a quadrilateral with two equal and two unequal sides. The important characteristics of a kite are as follows.

• Two pairs of adjacent sides are equal.
• One pair of opposite angles are equal.
• The diagonals of a kite are perpendicular to each other.
• The longer diagonal of the kite bisects the shorter diagonal.
• The area of a kite is equal to half of the product of the length of its diagonals.
• The perimeter of a kite is equal to the sum of the length of all of its sides.
• The sum of the interior angles of a kite is equal to 360°.

What are the Properties of the Diagonals of a Kite?

There are two diagonals in a kite that are not of equal length. The important properties of kite diagonals are as follows:

• The two diagonals of a kite are perpendicular to each other.
• One diagonal bisects the other diagonal.
• The shorter diagonal of a kite forms two isosceles triangles.
• The longer diagonal of a kite forms two congruent triangles.

Does a Kite Shape Have 4 Equal Angles?

No, a kite has only one pair of equal angles. The point at which the two pairs of unequal sides meet makes two angles that are opposite to each other. These two opposite angles are equal in a kite.

Does a Kite Shape Have a 90° Angle?

Yes, a kite has 90° angles at the point of intersection of the two diagonals. In other words, the diagonals of a kite bisect each other at right angles.

Can we say that a Kite is a Parallelogram?

No, a kite is not a parallelogram because the opposite sides in a parallelogram are always parallel, whereas, in a kite, only the adjacent sides are equal, and there are no parallel sides. Therefore, a kite is not a parallelogram.