Rhombus Lines of Symmetry Explanation with Examples (2023)

Rhombus has 2 lines of symmetry. Rhombus line of symmetry is the straight line along which a rhombus once folded obtains two symmetrical halves. A rhombus is a parallelogram geometric shape with all sides equal and the opposite sides parallel to each other. Diagonals of a rhombus bisect one another perpendicularly. The line of symmetry in mathematics is considered as a line that divides or splits a given shape into two identical halves.

What are Rhombus Lines of Symmetry?

A rhombus is a parallelogram geometric shape with all sides equal and the opposite sides parallel to each other. Also, the diagonals bisect one another perpendicularly. The straight line along which a rhombus once folded obtains two symmetrical halves is named the line of symmetry in the rhombus.

You can also understand this as lines of symmetry in a regular rhombus divide it into two identical halves such that each half is the mirror image of the other half.

Consider the diagram below, herein for the rhombus PQRS there will be two lines of symmetry as shown:

Rhombus Lines of Symmetry Explanation with Examples (1)

The first line of symmetry is along the diagonal SQ and the second line of symmetry is along the diagonal PR.

Rhombus Lines of Symmetry Explanation with Examples (2)

Here we can say that the diagonals are the 2 lines of symmetry in a rhombus. As when we fold the rhombus along any diagonal line, we obtain the identical shape as two halves.

Learn about Quadrilaterals

Lines of Rotational Symmetry in a Rhombus

For the different geometric shapes, symmetry is usually represented as the property of the object that remains unchanged even after a transformation. This transformation includes reflections, rotations, and translations.

When a given shape is rotated for a complete spin(360°) and the shape after the rotation is identical to the origin, we say that rotational symmetry exists. That is for rotational symmetry the initial shape and the shape obtained after one complete rotation should be the same.

A rhombus holds rotational symmetry of order 2 with the angle of rotation as 180 degrees. The image below shows the same:

Rhombus Lines of Symmetry Explanation with Examples (3)

From the figure, we can say that images of a rhombus are equal to the original or initial figure after rotating it twice (360°). Here each rotation is 180 degrees.

(Video) Lines of symmetry animation: Rhombus

Learn about Area of a Square

Rhombus Lines of Symmetry vs Square Lines of Symmetry

The term symmetry refers to the similarity of shapes in different orientations. A line of symmetry can be vertical, horizontal, or diagonal. Now that we know when the folded part of the given shape precisely superimposes on the other half of the shape, such that all the edges and corners are overlapping, then the folding line denotes a line of symmetry.

A shape can be symmetrical either along its length, width, or diagonals. When we compare a square and a rhombus, we can say that a square shape is a special case of a rhombus where all the internal angles are 90°. Thus a rhombus is also called a non-square rhombus as the measure of the internal angles is different in a rhombus.

As the square shape is a special case of a rhombus, let us understand if there is any difference in the no of lines of symmetry between the two. Consider, the below figure of a non-square rhombus, here as discussed earlier the number of lines of symmetry is 2. The symmetry lines are drawn via the diagonal.

Rhombus Lines of Symmetry Explanation with Examples (4)

Now consider the figure for the square; here the number of lines of symmetry is 4. Amongst the four lines of symmetry; two lines of symmetry are drawn via the diagonals and the rest are drawn through its vertical axis and horizontal axis respectively.

Rhombus Lines of Symmetry Explanation with Examples (5)

Learn about Polygons

Solved Examples on Rhombus Lines of Symmetry

Now that we can say that, a figure has a line of symmetry if the line can be drawn through the figure such that the figure is divided into two halves. Below are some questions based on rhombus lines of symmetry.

Example 1: Complete the statement with the suitable option.

The lines of symmetry in a rhombus are drawn_____?

(a) Base

(b) Diagonals

(c) Width

(Video) Shapes (Lines of Symmetry)

(d) Medians

Solution: The lines of symmetry in a rhombus are dawn via the diagonals. Thus option b is correct.

Example 2: A rhombus where all its interior angles are equivalent to 90°. The lines of symmetry are drawn on?
(a) Diagonals
(b) Horizontal axis and Vertical axis
(c) Diagonals, Horizontal and Vertical axis
(d) Diagonals and one of the axis

Solution: A rhombus where all its interior angles are equivalent to 90° forms a square. And in a square, the lines of symmetry are drawn on the diagonals, vertical as well as the horizontal axis. Thus option c is the most appropriate answer.

Example 3: Answer the below statements.
(a) The angles at which a rhombus contains rotational symmetry are?
(b)If one of the angles of a rhombus is an acute angle, how many lines will it have?
(c)How many lines of symmetry does a rectangle have?
(d) The number of lines of symmetry in an equilateral triangle is?

Solution: Let us start answering the questions one by one.

(a) The angles at which a rhombus contains rotational symmetry are?

A rhombus has rotational symmetry order of two, and the angle of rotation is 180 degrees.

(b)If one of the angles of a rhombus is an acute angle, how many lines of symmetry will it have?

As one of the angles is an acute angle i.e. less than 90 degrees, thus it is non a square-shaped rhombus. Thus the lines of symmetry=2.

(c)How many lines of symmetry does a rectangle have?

There are 2 lines of symmetry in a rectangle one on the horizontal axis and the other on the vertical axis.

(d) The number of lines of symmetry in an equilateral triangle is?

In an equilateral triangle will all three sides are of equal length there are 3 lines of symmetry drawn along the three medians.

(Video) What is Symmetry? - Basics | Line of Symmetry | Don't Memorise

We hope that the above article is helpful for your understanding and exam preparations. Stay tuned to the Testbook App for more updates on related topics from Mathematics, and various such subjects. Also, reach out to the test series available to examine your knowledge regarding several exams.

If you are checking Rhombus lines of symmetry article, also check the related maths articles:
Angle bisector theoremDividing fractions
Improper fractionGreatest common factor gcf
Multiplying fractionsFraction

FAQs on Rhombus Lines of Symmetry

Q.1What is a rhombus?

Ans.1 A rhombus is a parallelogram with all sides of equal dimensions and the angle between the diagonal is 90 degrees.

Q.2.What is the number of lines of symmetry in a rhombus?

Ans.2 . The number of lines of symmetry in a rhombus is two and these lines are drawn via the diagonals of a rhombus.

Q.3What is lines of symmetry?

Ans.3 Line of symmetry is considered as a line that divides or splits a given shape into two identical halves.

Q.4Do rhombuses have 2 pairs of parallel sides?

(Video) GCSE Maths - Types of Quadrilateral #101

Ans.4 Yes, a rhombus has two pairs of parallel lines such that there are 4 equal sides and the opposite sides are parallel to one another.

Q.5How many lines of symmetry does a square have?

Ans.5 A square has four lines of symmetry one on the vertical axis and horizontal axis and two through the diagonal lines.

Q.6What is the order of rotational symmetry of a rhombus?

Ans.6 A rhombus holds a rotational symmetry of order 2 as exactly after two rotations of 180 degrees the same shape is obtained.

(Video) Reflectional Symmetry and Rotational Symmetry | Don't Memorise

Videos

1. Line of symmetry (2D shapes) : used "paper-cut-out shape" to explain
(O-Level Mathematics)
2. Line Of Symmetry | Mathematics Grade 4 | Periwinkle
(Periwinkle)
3. GCSE Maths from Scratch 18.05a Lines of Symmetry
(TLMaths)
4. Joyful Learning of Mathematics| Exploring Rotational Symmetry in quadrilaterals using GeoGebra
(Mathematics Learning)
5. Why Does a Square Rectangle & Rhombus Have Rotational Symmetry? : Algebra, Geometry & More
(eHowEducation)
6. Rhombus Definition and Properties-Geometry
(MooMooMath and Science)
Top Articles
Latest Posts
Article information

Author: Lilliana Bartoletti

Last Updated: 07/08/2023

Views: 5251

Rating: 4.2 / 5 (53 voted)

Reviews: 92% of readers found this page helpful

Author information

Name: Lilliana Bartoletti

Birthday: 1999-11-18

Address: 58866 Tricia Spurs, North Melvinberg, HI 91346-3774

Phone: +50616620367928

Job: Real-Estate Liaison

Hobby: Graffiti, Astronomy, Handball, Magic, Origami, Fashion, Foreign language learning

Introduction: My name is Lilliana Bartoletti, I am a adventurous, pleasant, shiny, beautiful, handsome, zealous, tasty person who loves writing and wants to share my knowledge and understanding with you.