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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)
