Properties of Kite
A kite is a quadrilateral that has 2 pairs of equal adjacent sides. The angles where the adjacent pairs of sides meet are equal. There are two types of kites convex kites and concave kites. Convex kites have all their interior angles less than 180°, whereas, concave kites have at least one of the interior angles greater than 180°. This page discusses the properties of a convex kite.
1.  What are the Properties of Kite? 
2.  Properties of the Diagonals of a Kite 
3.  Solved Examples on Properties of Kite 
4.  Practice Questions on Properties Of Kite 
5.  FAQs on Properties Of Kite 
What are the Properties of Kite?
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 ABCD to relate to its properties given below.
 \(\angle ABC\)
 \(\angle BCD\)
 \(\angle CDA\)
 \(\angle DAB\)
 Side AB
 Side BC
 Side CD
 Side AD
 Diagonal AC
 Diagonal BD
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°.
Properties of the Diagonals of a Kite
As we have discussed in the earlier section, a kite has 2 diagonals. The important properties of kites with respect to their diagonals 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?
Topics Related to Properties of Kite
Check out some interesting articles related to the properties of a kite.
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.
 If the two adjacent sides of a kite are labeled as 'side 1' and 'side 2', then the perimeter of the kite is 2 (side 1 + side 2).
 The area of a kite is half the product of its diagonals.
Solved Examples on Properties of Kite

Example 1: Observe the kite given below and answer the following questions:
(a) If AB = 7 units, what is the measure of AC?
(b) If CD = 13 units, what is the measure of BD?
(c) If ∠B = 118°, then what is the measure of ∠C?
Solution:
(a) We know that two pairs of adjacent sides of a kite are equal. In the kite ABCD, AB = AC and BD = DC. Since the length of AB is known to be 7 units, AC = 7 units.
(b) Also, since the length of DC is 13 units, the length of BD is also 13 units.
(c) As per the properties of a kite, one pair of opposite angles are equal. In the kite ABCD, ∠B = ∠C. Since the measure of ∠B is known to be 118°, ∠C is also equal to 118°.

Example 2: Find the area and perimeter of the kite shown below, where side AB = 5 units, side BD = 26 units, AE = 10 units, ED = 24 units, BE = 12 units, EC = 12 units.
Solution:
Given: the length of the horizontal diagonal BC = 12 + 12 = 24 units; and the length of diagonal AD = 10 + 24 = 34 units.
The area of a kite = 1/2 × length of diagonal 1 × length of diagonal 2. Therefore, the area of the kite = 1/2 × 24 × 34 = 12 × 34 = 408 square units.
The perimeter of a kite = sum of the length of all sides of the kite. The sides of the kite are AB, AC, BD, and DC. From the kite, we observe that AB = 5 units, and from the properties of the kite, we know that adjacent pairs of sides are equal. Therefore, from the kite ABCD, AB = AC, therefore, AC is also equal to 5 units. Since BD = 26 units DC is also equal to 26 units. Therefore, the perimeter of the kite = AB + AC + BD + DC, which is equal to 5 + 5 + 26 + 26 = 62 units.
FAQs on Properties of Kite
What are the Properties of a Kite?
A kite is a quadrilateral with two equal and two unequal sides. The important properties of the 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:
 The two diagonals of a kite are perpendicular to each other.
 One diagonal bisect 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 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 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.