# Expert Maths Tutoring in the UK

(Geometry) Line Symmetry and Rotational Symmetry Lesson
(Geometry) Line Symmetry and Rotational Symmetry Lesson

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Reflection Symmetry

Reflective symmetry is a type of symmetry where one-half of the object reflects the other half of the object. It is also known as mirror symmetry. For example, in general, human faces are identical on the left and right sides. The wings of most butterflies are identical on both sides, the left and right sides.

 1 What is Reflection Symmetry? 2 Reflection Symmetry Examples 3 FAQs on Reflection Symmetry

## What is Reflection Symmetry?

Reflection symmetry is a type of symmetry about reflections. Even if there exists at least one line that divides a figure into two halves such that one-half is the mirror image of the other half, it is known as reflection symmetry. It is also known as line symmetry. The line of symmetry can be in any direction, horizontal, vertical, slanting, etc.

### Recognizing Reflection Symmetry

The very first thing to check is that one half should be the reflection of the other half. Imagine folding a rectangle along each line of symmetry and each of the half matching up perfectly, this is symmetry. Thus, a shape has to have at least one line of symmetry to be considered as a shape with reflection symmetry. Also, there is one most important property of reflection symmetry – For the two halves which are symmetrical, one of them follows lateral inversion, that is left side appears to be the right side as it happens when you look in a mirror.

## Reflection Symmetry Examples

Some of the common examples of reflection symmetry are given below:

• A square has 4 lines of symmetry, which are lines through the midpoints of opposites sides, and lines through opposite vertices make up the four lines of symmetry.
• A rectangle has two lines of symmetry, that is lines through the midpoints of opposites sides.
• A generic trapezoid will certainly not have reflection symmetry but an isosceles trapezoid will have reflection symmetry as the line connecting the midpoints of the bases make up a line of symmetry.
• The reflection of trees in clear water, the reflection of mountains in a lake are amongst the commonly seen examples of reflection symmetry around us.

Important Notes

• All regular polygons are symmetrical in shape.
• An object and its image are symmetrical with respect to its mirror line.
• Reflection symmetry can also be observed in inkblot paper.
• A figure can have one or more lines of reflection symmetry depending on its shape and structure.

### Topics Related to Reflection Symmetry

Check out these interesting articles to know about reflection symmetry and its related topics.

## Examples on Reflection Symmetry

1. Example 1: If k and l are the lines of reflection symmetry, complete the following figure.

Solution:

k and l are the lines of reflection symmetry, so we will make a leaf on the left side of the same size and shape as on the right side but yes following lateral inversion. (we could have also made leaf following lateral inversion downwards or even diagonally as k and l, both are lines of symmetry)

2. Example 2: Look at the shape on the left side and identify how the shape has been transformed.

• (a) Rotation
• (b) Reflection

Solution:

These images are depicting one most important property of reflection symmetry – The first image on the left follows lateral inversion, that is left side appears to be the right side as it happens when you look in a mirror. Therefore, it shows reflection symmetry.

## FAQs on Reflection Symmetry

### What is Meant by Reflection Symmetry?

When a shape or pattern is reflected in a line of symmetry or forms a mirror image, then it is considered to show reflection symmetry.

### What does Reflection Symmetry Look Like?

For any shape, reflection symmetry looks when a central dividing line (a mirror line) can be drawn on it, proving that both sides of the shape are exactly the same or reflections of one another.

### Does a Square have Reflection Symmetry?

Yes, a square has a reflection symmetry having four lines of reflection, two on midpoints on the sides and two through the opposite vertices (diagonals).

### Do Lines of Symmetry have to be Straight?

In most cases, the lines of symmetry are straight only. Although lines can be horizontal, vertical, or slanting. Also, a straight line has infinite lines of symmetry.

### How Many Lines of Reflection Symmetry does a Rectangle Have?

A rectangle is a regular polygon having two lines of symmetry and four sides.

### Does a Right Triangle have Reflection Symmetry?

A right-angled triangle doesn’t show reflection symmetry. It has no line of symmetry. It just has rotational symmetry of order 1.

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