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A kite is a 2D shape 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. It has two unequal diagonals perpendicular to each other.
Let’s understand how to construct a kite using a compass and ruler with steps and examples.
Construction of Kite in Geometry
A kite is a quadrilateral with two pairs of adjacent sides equal and the diagonals perpendicular to each other and one of the diagonals bisects the other. The diagonals of a kite are unequal (the longer one is called a major diagonal and the shorter one is called a minor diagonal). There are two methods of constructing a kite depending on the parameter known for construction. You can construct a unique kite when two unequal sides and a diagonal (major or minor) are given.
Construction of Kite in Geometry When Two Unequal Sides and a Diagonal is Given
The following are the steps are used in the construction of kite in geometry with given adjacent sides and a diagonal.
Step 1: Draw a line $\text{AC}$ (the diagonal) of given length
Step 2: Construct a perpendicular bisector $\text{XY}$ of $\text{AC}$
Read to understand the steps of construction of a perpendicular bisector of a line segment.
Step 3: With $\text{A}$ and centre and radius equal to the length of the smaller side draw an arc intersecting $\text{XY}$ at $\text{D}$
Step 4: With $\text{A}$ and centre and radius equal to the length of the longer side draw an arc intersecting $\text{XY}$ on the opposite side at $\text{B}$
Step 5: Join the points $\text{A}$ and $\text{B}$, $\text{B}$ and $\text{C}$, $\text{C}$ and $\text{D}$, $\text{D}$ and $\text{A}$
$\text{ABCD}$ is the required kite.
Practice Problems
- What is a kite in geometry?
- What are the properties of a kite?
- Construct a kite $\text{MADE}$ if $\text{AE} = 8 \text{ cm}$, $\text{ME} = 4 \text{ cm}$ and $\text{DE} = 6 \text{ cm}$. Which properties of the kite did you use in the process?
FAQs
Which properties of a kite are used in its construction?
The following properties of a kite are used in its construction:
a) Diagonals are at right angles
b) One of the diagonal bisects the other
c) Pairs of consecutive sides are equal
Which condition is used in the construction of a kite easy?
A quadrilateral is a kite if and only if any one of the following conditions is true
a) The four sides can be split into two pairs of adjacent equal-length sides.
b) One diagonal crosses the midpoint of the other diagonal at a right angle, forming its perpendicular bisector.
Conclusion
A kite is a quadrilateral with two pairs of adjacent sides equal and the diagonals perpendicular to each other and one of the diagonals bisects the other. You can construct a unique kite if you know the length of the two adjacent sides and one of the diagonals.
Recommended Reading
- How to Construct a Rectangle Using Compass and Ruler – Methods, Steps & Examples
- How to Construct a Square Using Compass and Ruler – Methods, Steps & Examples
- Construction of Trapezium Using Compass and Ruler – (Methods, Steps & Examples)
- How to Construct a Rhombus Using Compass and Ruler – (Methods, Steps & Examples)
- How to Construct a Rectangle Using Compass and Ruler – Methods, Steps & Examples
- How to Construct a Square Using Compass and Ruler – Methods, Steps & Examples
- What is a Scalene Triangle – Definition, Properties & Examples
- What is an Isosceles Triangle – Definition, Properties & Examples
- What is an Equilateral Triangle – Definition, Properties & Examples
- What is a Rectangle – Definition, Types, Properties & Examples
- What is a Rhombus – Definition, Types, Properties & Examples
- What is a Trapezium – Definition, Types, Properties & Examples
- What is a Parallelogram – Definition, Properties & Examples
- Types of Quadrilaterals and Their Properties(With Definitions & Examples)
- What is Quadrilateral in Math(Definition, Shape & Examples)
