How to Construct a Rhombus Using Compass and Ruler – (Methods, Steps & Examples)

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A rhombus(plural rhombi) is a special type of parallelogram in which opposite sides are parallel and the opposite angles are equal. Also, a rhombus’s sides are equal in length, and the diagonals bisect each other at right angles. These properties are used to construct a rhombus.

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

How to Construct a Rhombus?

A rhombus is a quadrilateral with all sides of equal length and opposite angles equal. The two diagonals of a rhombus are unequal and bisect each other at a right angle. There are three methods of constructing a rhombus depending on the parameter known for construction. You can construct a unique rhombus when

• one side and one angle are given
• one side and one diagonal are given
• both the diagonals are given

How to Construct a Rhombus When One Side and One Angle Are Given

Since all four sides of a rhombus are equal and also the opposite angles are equal, therefore, you can construct a unique rhombus if the length of one side and one angle is known.

The following are the steps to construct a unique rhombus with given one side and one angle.

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

Step 2: Construct the given angle at $\text{A}$, $\angle \text{BAX}$.

Step 3: With $\text{A}$ as the centre and radius equal to the given length of a rhombus, draw an arc on ray $\text{AX}$. Mark the point of intersection as $\text{D}$.

Step 4: With $\text{D}$ as the centre and radius equal to the given length of a rhombus, draw an arc

Step 5: With $\text{B}$ as the centre and the same radius, draw another arc such that it intersects the previous arc at $\text{C}$

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

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

How to Construct a Rhombus When Two Diagonals Are Given

Since the diagonals of a rhombus are perpendicular to each other and bisect each other, therefore, you can construct a unique rhombus if the length of two diagonals is known.

The following are the steps to construct a unique rhombus with given two diagonals.

Step 1: Draw line segment $\text{AC}$  equal to the length of first diagonal

Step 2: Draw the perpendicular bisector of $\text{AC}$

Step 3: With $\text{O}$ as the centre and radius equal to half the length of the second diagonal, mark arcs on both sides of $\text{AC}$ to intersect its perpendicular bisector. Mark the points of intersection as $\text{B}$ and $\text{D}$

Step 4: Join points $\text{A}$, $\text{D}$, points $\text{C}$, $\text{D}$, points $\text{C}$, $\text{B}$, and points $\text{B}$, $\text{A}$

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

How to Construct a Rhombus When One Side and One Diagonal Are Given

Since the diagonal and the side of a rhombus forms a right triangle, therefore, you can construct a unique rhombus if the length of a side and the diagonal is known.

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

Step 1: Draw a line segment $\text{AB}$ equal to given side of a rhombus

Step 2: With $\text{B}$ as the centre and radius equal to the length of the side of a rhombus, draw an arc

Step 3: With $\text{B}$ as the centre and radius equal to the length of the diagonal, draw another arc such that it intersects the previous arc at $\text{C}$

Step 4: Join points $\text{B}$, $\text{C}$ and points $\text{A}$, $\text{C}$

Step 5: With $\text{A}$ as the centre and radius equal to the length of the side of a rhombus, draw an arc

Step 6: With $\text{C}$ as the centre and the same radius, draw another arc such that it intersects the previous arc at $\text{D}$

Step 7: Join points $\text{D}$, $\text{A}$ and points $\text{D}$, $\text{C}$

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

Practice Problems

1. What is a rhombus in geometry?
2. Construct a rhombus whose side is $5 \text{cm}$ and the measure of one angle is $60^{\circ}$.
3. Construct a rhombus whose two diagonals are of length are $10 \text{cm}$ and $12 \text{cm}$.
4. Construct a rhombus whose one side and one diagonal are of length $5 \text{cm}$ and $13 \text{cm}$ respectively.

Conclusion

A rhombus is a quadrilateral with all sides of equal length and opposite angles equal. You can construct a unique rhombus if it’s one side and one angle or both the diagonals or one side and one diagonal are known.

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