Is A Square A Kite

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. At that place are two types of kites - convex kites and concave kites. Convex kites have all their interior angles less than 180°, whereas, concave kites take at least 1 of the interior angles greater than 180°. This page discusses the backdrop of a convex kite.

1.	What is a Kite Shape?
ii.	What are the Properties of Kite?
3.	Diagonals of a Kite
4.	FAQs on Properties Of 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 only ane pair of opposite angles are equal. Let the states learn more than about the properties of a kite.

What are the Backdrop 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. Find the following kite ACBD to relate to its properties given below. Kite shape

Nosotros can identify and distinguish a kite with the assist of the post-obit properties:

A kite has two pairs of adjacent equal sides. Here, Air conditioning = BC and Advertisement = BD.
Information technology has i pair of reverse angles (obtuse) that are equal. Here, ∠A = ∠B
In the diagonal AB, AO = OB.
The shorter diagonal forms 2 isosceles triangles. Here, diagonal 'AB' forms 2 isosceles triangles: ∆ACB and ∆ADB. The sides Air-conditioning and BC are equal and AD and BD are equal which form the ii 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 3 sides of ∆CAD are equal to the lengths of three sides of ∆CBD.
The diagonals are perpendicular to each other. Hither, AB ⊥ CD.
The longer diagonal bisects the shorter diagonal.
The longer diagonal bisects the pair of opposite angles. Hither, ∠ACD = ∠DCB, and ∠ADC = ∠CDB
The area of a kite is half the production of its diagonals. (Expanse = 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 ii diagonals. The important properties of the diagonals of a kite are given below.

The 2 diagonals are not of the same length.
The diagonals of a kite intersect each other at correct angles. It tin exist observed that the longer diagonal bisects the shorter diagonal.
A pair of diagonally opposite angles of a kite are said to be coinciding.
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 side by side coinciding sides.
The longer diagonal of a kite forms two congruent triangles past the SSS property of congruence. This is because the 3 sides of 1 triangle to the left of the longer diagonal are congruent to the sides of the triangle to the correct of the longer diagonal.

Challenging Questions

Can a kite be chosen a parallelogram?
Can a kite have sides of 12 units, 25 units, thirteen units, and 25 units?

Important Notes

Some of import points well-nigh a kite are given below.

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

☛Related Articles

Measurement
Expanse of a Kite
Types of Quadrilaterals
Congruence in Triangles
SSS Formula

Examples on Backdrop of Kite

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

(a) If AB = seven units, what is the length of Air conditioning?

(b) If CD = thirteen units, what is the length of BD?

(c) If ∠B = 118°, then what is the measure of ∠C?

Solution:

(a) We know that 2 pairs of next sides of a kite are equal. In the kite ABCD, AB = AC and BD = DC. Since the length of AB is known to exist seven units, AC = 7 units.

(b) As well, since the length of DC is 13 units, the length of BD is besides xiii units.

(c) Equally per the backdrop of a kite, 1 pair of opposite angles are equal. In the kite ABCD, ∠B = ∠C. Since the mensurate of ∠B is known to be 118°, ∠C is likewise equal to 118°.
Example 2: Find the area of a kite if its diagonals are of the length 12 units and 5 units respectively.

Solution: The surface area of a kite can be calculated if the length of its diagonals is known. So, Expanse of a kite = 1/2 × diagonal one × diagonal ii. After substituting the values we get, Surface area of a kite = 1/2 × 12 × 5 = 30 unitⁱⁱ
Case 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 aforementioned length.

Solution:

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

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

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Practice Questions on Properties of Kite

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FAQs on Properties of Kite

What is a Kite in Geometry?

In Geometry, a kite is a quadrilateral in which ii pairs of side by side 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 1 that does not look like a parallelogram or a rectangle considering none of its sides are parallel to each other. It is symmetrical in shape and can be imagined as the existent kite which was used for flying in the olden days.

How to Find the Expanse of a Kite?

The surface area of a kite is the space occupied by it. It can be calculated using the formula, Area of kite = ane/2 × diagonal 1 × diagonal two. For instance, if the length of the diagonals of a kite are given as 7 units and four units respectively, we can find its surface area. After substituting the values in the formula, we become, Area of kite = 1/2 × 7 × 4 = 14 unit of measurement²

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 ane 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 non of equal length. The of import backdrop of kite diagonals are as follows:

The 2 diagonals of a kite are perpendicular to each other.
One diagonal bisects the other diagonal.
The shorter diagonal of a kite forms 2 isosceles triangles.
The longer diagonal of a kite forms two congruent triangles.

Does a Kite Shape Have 4 Equal Angles?

No, a kite has merely one pair of equal angles. The point at which the two pairs of diff sides meet makes 2 angles that are contrary to each other. These two opposite angles are equal in a kite.

Does a Kite Shape Accept a 90° Angle?

Yes, a kite has 90° angles at the bespeak 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 considering 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.

Is A Square A Kite,

Source: https://www.cuemath.com/geometry/properties-of-kite/

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