108 LearnersLast updated on July 15th, 2025
Properties of Kite
A kite is a type of quadrilateral that has a lot of unique properties. These properties help students simplify geometric problems related to kites. The properties of a kite are: it is supposed to have two distinct pairs of adjacent sides that are equal in length and the diagonals of the kite intersect at right angles. These properties help students to analyze and solve problems related to symmetry, angles, and area. Now let us learn more about the properties of a kite.
What are the Properties of a Kite?
The properties of a kite are simple, and it helps students to understand and work with this type of quadrilateral. These properties are derived from the principles of geometry.
There are several properties of a kite and some of them are mentioned below:
- Property 1: Two pairs of equal sides
The kite has two distinct pairs of adjacent sides that are equal in length.
- Property 2: One pair of equal angles
The angles formed between any two unequal sides are equal.
- Property 3: Diagonals
Both the diagonals of the kite intersect at right angles.
One of the diagonals of the kite bisects the other which divides the diagonal into two equal parts.
- Property 4: Symmetry
The kite has one line of symmetry along the longer diagonal.
- Property 5: Area Formula
The formula used to calculate the area of the kite is given below:
Area = ½ x d1 x d2
Here, the lengths of the diagonals are represented as d1 and d2.
Tips and Tricks for Properties of a Kite
Students tend to confuse and make mistakes while learning the properties of a kite. To avoid such confusion, we can follow the following tips and tricks:
Two Pairs of Adjacent Sides are equal:
Students should remember that in a kite, two pairs of sides that are adjacent are equal in length. To verify this, the students can draw a kite shaped quadrilateral and see that the two adjacent sides in the diagram that they drew are equal in length.
Diagonals are Perpendicular:
Students should remember that in a kite, the diagonals always intersect at right angles.
Longer Diagonal Bisects the Shorter Diagonal:
Students should remember that in a kite, the longer diagonal always cuts the shorter diagonal exactly into two equal parts.
Common Mistakes and How to Avoid Them in Properties of Kites
Students tend to get confused when understanding the properties of a kite, and they tend to make mistakes while solving problems to said properties. Here are some common mistakes the students tend to make and the solutions to said common mistakes.
Mistake 1
Confusing a Kite with a Rhombus
Students should remember that a kite has adjacent sides that are equal. Whereas, in rhombus, all sides are equal.
Mistake 2
Misinterpreting the Diagonal Relationship
Students should know and remember that the longer diagonal bisects the shorter diagonal and divides it into two equal halves, and that in a kite, the diagonals intersect at right angles.
Mistake 3
Incorrectly Applying the Formula
Students should practice the formula which is used to find the area of a kite, which is given below. The students must also understand the representations of d1 and d2.
Area = ½ x d1 x d2
Mistake 4
Misunderstanding Angle Relationships
Students should remember that one set of opposite angles are equal. And those angles are between the unequal sides.
Mistake 5
Forgetting the Unequal Side Rule
Students must remember that a kite must have exactly two pairs of adjacent sides which are equal in length.
Solved Examples on the Properties of Kites
Problem 1
In a kite, the four corners are marked as A, B, C, and D. If AB = 4cm, BC = 7cm, and AD = 4cm, then what is the length of the side CD?
CD = 7cm.
Explanation
In a kite, two pairs of adjacent sides are equal.
Since AB = 4cm and AD = 4cm, then BC = CD
Hence, CD = 7cm.
Problem 2
In a kite ABCD, the angle ABC = 110 degrees. What is the measure of angle ADC?
ADC = 110 degrees
Explanation
In a kite, students should know that there are multiple angles but only one pair of angles are equal.
Here, the angles ABC and ADC are opposite.
Hence, angle ADC = 110 degrees.
Problem 3
The diagonals of a kite intersect at point O. If angle AOB = 90 degrees, what can you conclude about the diagonals of the kite?
Diagonals of the kite are perpendicular to each other.
Explanation
The angle AOB is 90 degrees. According to a property of kites, the diagonals of a kite are perpendicular to each other.
Problem 4
In kite ABCD, diagonal AC bisects diagonal BD at a point E. If BE = 3cm, what is the length of ED?
ED = 3cm
Explanation
Since BE = 3cm and the longer diagonal AC bisects BD, then ED = BE = 3cm.
Problem 5
A kite has diagonals of length 8cm and 10cm. What is the area of the kite?
Area = 40 sq cm.
Explanation
Applying the formula, area = ½ x d1 x d2
Substituting the values to the formula, we get
Area = ½ x 8 x 10 = 40 cm2.
FAQs on Properties of Kites
1.What is a kite in geometry?
2.How many pairs of equal sides does a kite have?
3.Are all sides of a kite equal?
4.How do you find the area of a kite?
5.Can a kite have all four sides equal?
Important Glossaries for the Properties of a Kite
- Quadrilateral: A kite is a four-sided polygon, which is a type of quadrilateral.
- Adjacent Sides: In a kite, two pairs of adjoining or so called as adjacent sides are equal in length.
- Diagonals: The diagonals of a kite are lines that connect one point to another point opposite to it.
- Diagonal Bisector: In a kite, the longer diagonal of the kite bisects the shorter diagonal and divides it into two equal halves.
- Opposite Angles: In a kite, there is only one pair of opposite angles which are equal in measure.
Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
