## What Are the Properties of a Kite?

**Properties of a kite are the distinct characteristics or features of the kite shape, its vertices, interior angles, sides, diagonals that makes it a unique shape. **

You’re probably familiar with a kite as a fun paper toy that soars high in the sky wherever the wind carries it. The kite is constructed based on a geometrical shape called a “kite.” Let’s explore the definition of kite and its properties in geometry.

#### Begin here

## What Is a Kite Shape?

A kite is a quadrilateral, a closed flat geometric shape in which two sets of neighboring or adjacent sides are congruent (equal in length). Its diagonals meet at right angles.

**There are two types of kites.**

**Convex: **Each interior angle measures less than $180^\circ$.

**Concave: **One interior angle is greater than $180^\circ$. A dart or an arrowhead is an example of a concave kite.

#### Related Worksheets

## Properties of a Kite

Let’s learn the important properties of a kite in geometry using the following diagram. We will discuss side properties of a kite as well as diagonal properties of a kite.

Here, the longer diagonal RS is referred to as the main or primary diagonal.

- Two pairs of adjacent sides are equal. $\left[ PR = QR,\; PS = QS \right]$
- Two diagonals intersect each other at right angles. $\left[ PQ \;\bot\; RS \right]$
- The kite is symmetrical about the longer diagonal.
- The longer diagonal bisects the shorter diagonal. $\left[ OP = OQ \right]$
- The angles opposite to the main diagonal are equal. $\left[\angle P = \angle Q\right]$
- The kite is split into two isosceles triangles by the shorter diagonal.

$[\Delta PRQ \;and\; \Delta PSQ]$

- The kite is divided into two congruent triangles by the longer diagonal.

$[\Delta PRS \;and\; Delta QRS]$

- The longer diagonal bisects the pair of opposite angles.

$\left[\angle PRS = \angle QRS, \;and\; \angle PSR = \angle QSR\right]$

- The area of kite $= \frac{1}{2} \times d_1 \times d_2$, where $d_1,\; d_2$ are lengths of diagonals.
- Perimeter of a kite with sides a and b is given by $2\left[a+b\right]$.
- The sum of the interior angles of a kite $= 360^\circ$.

## Properties of Diagonals of a Kite

- Two diagonals of the kite are perpendicular to each other. Thus, KT and IE intersect at right angles.
- They are not equal in length. $\left[KT\; IE\right]$
- The longer diagonal bisects the shorter diagonal. $\left[OK = OT\right]$
- Angles opposite to the longer diagonal are congruent. $\left[\angle K = \angle T\right]$

## Fun Facts About Properties of a Kite!

- When all the sides of a kite are congruent, it becomes a rhombus.
- Kite is referred to as a dart when it’s not convex.
- When all sides are congruent and all interior angles measure 90 degrees, the kite becomes a square.
- A kite has all the properties of a cyclic quadrilateral.
- The product of a kite’s diagonals is equal to half of its area.

## Conclusion

A kite is a quadrilateral form with two pairs of adjacent sides that are congruent. Let’s solve a few examples for better understanding.

**Solved Examples on Properties of a Kite**

**Find the area of a kite whose diagonals are 6 and 18 inches long.**

**Solution:**

Area of a kite $= \frac{d_1\;d_2}{2}$

$= \frac{(6\times18)}{2}$

$= 54$ square inches.

**Find:**

**a) PR **

**b) RS **

**c) **$\angle C$

**Solution:**

- Two pairs of adjacent sides of a kite are equal. In the kite PQRS, $PQ = PR \;and\; QS = RS$.

Since $PQ = 5$ units, $PR = 5$ units.

- Similarly, $RS = QS = 10$ units
- Angles opposite to the main diagonal are equal. $\angle C = \angle B = 109^\circ$

**Four friends are flying identical-sized kites at a park. Each kite has diagonals of 12 inches and 15 inches. Find the total area of four kites combined together.**

**Solution:**

Lengths of diagonals are:

$d_1 = 12$ in

$d_2 = 15$ in

The area of each kite is:

$A = \frac{1}{2} \times d_1 \times d_2$

$= \frac{1}{2} \times 12 \times 15$

$= 90 \;in^2$

Since each kite is the same size, their combined area is equal to $4\times90 = 360 \;in^2$.

The four kites’ combined surface area is $360 \;in^2$.

**Mike wants to offer his pal a kite-shaped chocolate box. He plans to cover the box’s top with a photo of himself and his friend. Find the area of the box’s top if the lid’s diagonals are****9 in****and****12 in****.**

**Solution:**

d₁=9 in

d₂=12 in

The area of the box’s top is equal to since the box is shaped like a kite.

$A = \frac{1}{2} \times d_1 \times d_2$

$A = \frac{1}{2} \times 9 \times 12$

Thus, the box’s top surface area is $54\;in^2$

**Find the unknown angles of the given kite.**

**Given that:**

$\angle JKL = 130^\circ$

$\angle JML = 50^\circ$

Angles opposite to the main diagonal are congruent.

$\angle KJM = \angle KLM$

Hence, $\angle KLM = 130^\circ$

The sum of all angles of the quadrilateral $= 360^\circ$.

$130^\circ + 130^\circ + 50^\circ + \angle JML = 360^\circ$

$\angle JML = 50$

## Practice Problems on Properties of a Kite

## Properties of a Kite: Definition, Examples, Facts, FAQs

### A kite has an area of $126\; inches^2$ with a diagonal that is 21 inches long. Determine the length of the other diagonal.

Since the area of a kite is given by $A = \frac{1}{2} \times d_1 \times d_2$

So, $126, \text{inches}^2 = \frac{1}{2} \times 21 \times d_2$

Length of the other diagonal $= 12$ inches.

### The diagonals of a kite are ________.

Diagonals of a kite are perpendicular.

### Find the perimeter of a kite whose sides are 21 inches and 15 inches.

Since the perimeter of the kite$= 2(a + b) = 2(21 + 15) = 72$ inches.

### If a kite's diagonals are 12 units and 5 units respectively, what is its area?

Since area of kite $= \frac{1}{2}\times d_1 \times d_2 = 12\times12\times5 = 30\; units^2$.

### Each interior of a convex kite is __________.

Each interior angle of a convex kite measures less than $180^\circ$.

## Frequently Asked Questions on Properties of a Kite

**Is every kite a rhombus?**

No, all kites are not rhombuses. When all sides of a kite are congruent, it becomes a rhombus.

**Which quadrilateral has properties of a kite and a parallelogram?**

Rhombus

**Is a kite a parallelogram?**

No, a kite is not a parallelogram. The opposite sides in a parallelogram are parallel. In a kite, there are no parallel sides.

**How many lines of symmetry does a kite have?**

A kite has only one line of symmetry, which is the longer diagonal.

**What are the four important properties of a kite?**

- Two pairs of adjacent sides are equal.
- Two diagonals intersect each other at right angles.
- The longer diagonal bisects the shorter diagonal.
- The angles opposite to the main diagonal are equal.