How to Construct a Rectangle Using Compass and Ruler – Methods, Steps & Examples

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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

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

FAQs

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.

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