This post is also available in: हिन्दी (Hindi)

A rectangle is a closed 2D shape with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to $90^{\circ}$.

Let’s understand how to construct a rectangle using compass and ruler with steps and examples.

## How to Construct a Rectangle Using Compass and Ruler?

A rectangle is a quadrilateral with opposite sides of equal length and angles of the same measure of $90^{\circ}$. There are three methods of constructing a rectangle depending on the parameter known for construction. You can construct a unique rectangle if

- length of two adjacent sides is known
- length of a side and a diagonal is known
- length of one diagonal and the angle between the two diagonals is known

### How to Construct a Rectangle With Two Given Sides?

Since the two adjacent sides of a rectangle are perpendicular to each other and also the opposite sides are equal, therefore, you can construct a unique rectangle if the length of the adjacent sides is known.

The following are the steps to construct a unique rectangle with given two adjacent sides.

**Step 1:** Draw a side $\text{AB}$ of a given length

**Step 2:** Draw a perpendicular $\text{AE}$ to $\text{AB}$ at the point $\text{A}$

Read to know how to draw a perpendicular line.

**Step 3:** Draw a perpendicular $\text{BF}$ to $\text{AB}$ at the point $\text{B}$

**Step 4:** With the help of a compass, cut an arc of the length of the adjacent side on $\text{AE}$ at $\text{D}$

**Step 5:** With the help of a compass, cut an arc of the length of the adjacent side on $\text{BF}$ at $\text{C}$

**Step 6: **Join the points $\text{B}$ and $\text{C}$, $\text{C}$ and $\text{D}$, $\text{D}$ and $\text{A}$

$\text{ABCD}$ is a rectangle where the adjacent sides are of length $\text{AB}$ and $\text{BC}$ respectively.

## How to Construct a Rectangle With Given One Side and One Diagonal?

Since the two diagonals of a rectangle are equal and bisect each other, therefore, you can construct a unique rectangle if the length of the one side and diagonal is known.

The following are the steps to construct a unique rectangle with given one side and one diagonal.

**Step 1:** Draw a line segment $\text{AB}$ of given length

**Step 2:** At $\text{B}$, draw $\text{BE} \perp \text{AB}$

**Step 3:** With $\text{A}$ as centre and radius equal to the length of the diagonal, draw an arc cutting $\text{BE}$ at $\text{C}$

**Step 4:** With $\text{B}$ as centre and radius equal to the length of the diagonal, draw an arc

**Step 5:** With $\text{C}$ centre and radius equal to the length of the side, another arc, cutting the previous arc at $\text{D}$.

**Step 6:** Join $\text{A}$ and $\text{D}$, $\text{C}$ and $\text{D}$

$\text{ABCD}$ is a rectangle where the side $\text{AB}$ and diagonal $\text{AC}$ of given length.

### How to Construct a Rectangle With Given One Diagonal and the Angle Between the Diagonals?

Since the two diagonals of a rectangle are equal and bisect each other, therefore, you can construct a unique rectangle if the length of a diagonal and the angle between the diagonals are known.

The following are the steps to construct a unique rectangle with given one diagonal and the angle between the diagonals.

**Step 1:** Draw the diagonal $\text{AC}$ of given length

**Step 2:** Draw the perpendicular bisector of $\text{AC}$ and locate the mid-point $\text{O}$ of $\text{AC}$

Read to know how to draw a perpendicular bisector.

**Step 3:** Through $\text{O}$, construct a line $\text{POQ}$ so that $\angle \text{POC}$ equal to the angle between the diagonals

**Step 4:** From $\text{O}$ cut $\text{OB}$ and $\text{OD}$ equal to half the length of diagonal given

**Note:** $\text{O}$ is the midpoint of the diagonals $\text{AC}$ and $\text{BD}$.

**Step 5:** Join $\text{A}$ with $\text{B}$, $\text{B}$ with $\text{C}$, $\text{C}$ with $\text{D}$ and $\text{D}$ with $\text{A}$.

$\text{ABCD}$ is a rectangle where the diagonal $\text{AC}$ of given length.

## Practice Problems

- What is a rectangle in geometry?
- Construct a rectangle whose adjacent sides are $5 \text{cm}$ and $8 \text{cm}$.
- Construct a rectangle whose adjacent sides are $5 \text{cm}$ and $8 \text{cm}$.
- Construct a rectangle whose one side and one diagonal are of length $4 \text{cm}$ and $7 \text{cm}$ respectively.
- Construct a rectangle whose diagonal is of length $8 \text{cm}$ and the angle between the diagonals is $60^{\circ}$.

## FAQs

### What is rectangle with diagram?

A rectangle is a closed 2D shape with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to $90^{\circ}$.

### What are the different methods of constructing a rectangle?

The different methods of constructing a rectangle are when

a) length of two adjacent sides is known

b) length of a side and a diagonal is known

c) length of one diagonal and the angle between the two diagonals is known

## Conclusion

A rectangle is a closed 2D shape with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to $90^{\circ}$. A unique rectangle can be constructed using compass and ruler when the length of two adjacent sides, the length of a side, and a diagonal or length of one diagonal and the angle between the two diagonals is known.

## Recommended Reading

- 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)
- Angle Bisector of a Triangle – Definition, Properties & Examples
- Similarity of Triangles Criteria – SSS, SAS, AA
- Congruence of Triangles Criteria – SSS, SAS, ASA, RHS
- Altitude of a Triangle(Definition & Properties)
- Median of a Triangle(Definition & Properties)
- How to Construct a Triangle(With Steps, Diagrams & Examples)
- Median of a Triangle(Definition & Properties)
- Altitude of a Triangle(Definition & Properties)
- Congruence of Triangles Criteria – SSS, SAS, ASA, RHS
- Similarity of Triangles Criteria – SSS, SAS, AA
- Angle Bisector of a Triangle – Definition, Properties & Examples
- What is Quadrilateral in Math(Definition, Shape & Examples)
- Properties of Triangle – Theorems & Examples
- Types of Triangles – Definition & Examples
- What is Triangle in Geometry – Definition, Shapes & Examples
- Pair of Angles – Definition, Diagrams, Types, and Examples
- Construction of Angles(Using Protractor & Compass)
- Types of Angles in Maths(Acute, Right, Obtuse, Straight & Reflex)
- What is an Angle in Geometry – Definition, Properties & Measurement
- How to Construct a Tangent to a Circle(With Steps & Pictures)
- Tangent of a Circle – Meaning, Properties, Examples
- Angles in a Circle – Meaning, Properties & Examples
- Chord of a Circle – Definition, Properties & Examples
- How to Draw a Circle(With Steps & Pictures)
- What is a Circle – Parts, Properties & Examples
- How to Construct a Perpendicular Line (With Steps & Examples)
- How to Construct Parallel Lines(With Steps & Examples)
- How To Construct a Line Segment(With Steps & Examples)
- What are Collinear Points in Geometry – Definition, Properties & Examples
- What is a Transversal Line in Geometry – Definition, Properties & Examples
- What are Parallel Lines in Geometry – Definition, Properties & Examples
- What is Concurrent lines in Geometry – Definition, Conditions & Examples
- What is Half Line in Geometry – Definition, Properties & Examples
- What is a Perpendicular Line in Geometry – Definition, Properties & Examples
- Lines in Geometry(Definition, Types & Examples)