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Construction of Kite Using Compass and Ruler – (Methods, Steps & Examples)

construction of kite in geometry

This post is also available in: हिन्दी (Hindi)

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.

construction of kite in geometry

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

construction of kite in geometry

Step 2: Construct a perpendicular bisector $\text{XY}$ of $\text{AC}$

construction of kite in geometry

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 $\text{D}$

construction of kite in geometry

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 $\text{B}$

construction of kite in geometry

Step 5: Join the points $\text{A}$ and $\text{B}$, $\text{B}$ and $\text{C}$, $\text{C}$ and $\text{D}$, $\text{D}$ and $\text{A}$

construction of kite in geometry

$\text{ABCD}$ is the required kite.

girl-with-teacher-happy
Maths can be really interesting for kids

Practice Problems

  1. What is a kite in geometry?
  2. What are the properties of a kite?
  3. 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.

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