In the figure ab is parallel to dc write two pairs of triangles which have equal area

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.

What is 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. Let us learn more about the properties of a 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 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°.

Diagonals of a Kite

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

1. Example 1: Observe the kite shape given below and answer the following questions:

   (a) If AB = 7 units, what is the length of AC?

   (b) If CD = 13 units, what is the length 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°.

2. Example 2: Find the area of a kite if its diagonals are of the length 12 units and 5 units respectively.

   Solution: The area of a kite can be calculated if the length of its diagonals is known. So, Area of a kite = 1/2 × diagonal 1 × diagonal 2. After substituting the values we get, Area of a kite = 1/2 × 12 × 5 = 30 unit2

3. Example 3: State true or false

   a.) The sum of the interior angles of a kite is equal to 360°.

   b.) The two diagonals are not of the same length.

   Solution:

   a.) True, the sum of the interior angles of a kite is equal to 360°.

   b.) True, the two diagonals are not of the same length.

View More >

go to slidego to slidego to slide

Breakdown tough concepts through simple visuals.

Math will no longer be a tough subject, especially when you understand the concepts through visualizations.

Book a Free Trial Class

FAQs on Properties of Kite

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 was used for flying in the olden days.

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 length 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 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 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.

Try the new Google Books

Check out the new look and enjoy easier access to your favorite features

One special kind of polygons is called a parallelogram. It is a quadrilateral where both pairs of opposite sides are parallel.

There are six important properties of parallelograms to know:

1. Opposite sides are congruent (AB = DC).
2. Opposite angels are congruent (D = B).
3. Consecutive angles are supplementary (A + D = 180°).
4. If one angle is right, then all angles are right.
5. The diagonals of a parallelogram bisect each other.
6. Each diagonal of a parallelogram separates it into two congruent triangles.
   

$$\triangle ACD\cong \triangle ABC$$

If we have a parallelogram where all sides are congruent then we have what is called a rhombus. The properties of parallelograms can be applied on rhombi.

If we have a quadrilateral where one pair and only one pair of sides are parallel then we have what is called a trapezoid. The parallel sides are called bases while the nonparallel sides are called legs. If the legs are congruent we have what is called an isosceles trapezoid.

In an isosceles trapezoid the diagonals are always congruent. The median of a trapezoid is parallel to the bases and is one-half of the sum of measures of the bases.

$$EF=\frac{1}{2}(AD+BC)$$

Video lesson

Find the length of EF in the parallelogram