Let's Learn Mathematics

Reflectional Symmetry

Introduction

Reflectional symmetry (also called line symmetry or mirror symmetry) occurs when one half of an object is the mirror image of the other half. If you can draw a line through an object so that one side is exactly the same as the other side, the object has reflectional symmetry.

Examples of shapes with reflectional symmetry

Understanding Reflectional Symmetry

A shape has reflectional symmetry if:

  • It can be divided into two identical halves
  • The two halves are mirror images of each other
  • The line dividing the shape is called the line of symmetry

Example: The letter "A" has one vertical line of symmetry.

Letter A with line of symmetry

Real-Life Examples

Symmetry in Nature

Many objects in nature exhibit reflectional symmetry:

Human Face

The human face is approximately symmetrical with one vertical line of symmetry

Human face symmetry

Leaves

Many leaves have one line of symmetry down the center

Leaf symmetry

Butterflies

Butterfly wings are symmetrical with one vertical line of symmetry

Butterfly symmetry

Symmetry in Architecture

Many buildings and structures are designed with reflectional symmetry:

Taj Mahal (India)

Taj Mahal symmetry

Traditional Ghanaian Houses

Ghanaian house symmetry

Symmetry in Designs

Adinkra Symbols

Many Adinkra symbols from Ghana exhibit reflectional symmetry:

Gye Nyame

This symbol has multiple lines of symmetry

Gye Nyame symbol

Sankofa

This symbol has one vertical line of symmetry

Sankofa symbol

Denkyem

This crocodile symbol has one vertical line of symmetry

Denkyem symbol

National Flags

Many national flags use reflectional symmetry in their designs:

Ghana Flag

Ghana flag

Horizontal symmetry

Canada Flag

Canada flag

Vertical symmetry

Creating Symmetry

Shading Squares for Symmetry

Let's explore how to create symmetry by shading squares in a grid:

Example 1

Given this shape, where can we shade one more square to create a line of symmetry?

Grid example 1

There are 2 possible squares that can be shaded to create vertical symmetry:

Grid solution 1

Example 2

How many ways can we shade one square to create horizontal symmetry here?

Grid example 2

There is only 1 square that can be shaded to create horizontal symmetry:

Grid solution 2

Identifying Lines of Symmetry

To determine if a shape has reflectional symmetry:

  1. Imagine folding the shape along a line
  2. Check if both halves match exactly
  3. Try different lines (vertical, horizontal, diagonal)
  4. Count how many different lines create matching halves

Example: A rectangle has 2 lines of symmetry (vertical and horizontal)

Rectangle symmetry lines

Practice Exercise

Question 1

Name 3 objects in your classroom that have reflectional symmetry.

Possible answers: door, window, book, ruler, desk, etc.

Question 2

How many lines of symmetry does the Adinkra symbol "Akoma" have?

Akoma symbol

Answer: 4 lines of symmetry (vertical, horizontal, and two diagonal)

Question 3

In how many different ways can you shade one more square in this shape to create a line of symmetry?

Grid problem

Answer: 3 ways (creating vertical, horizontal, or diagonal symmetry)

Grid solution

Question 4

Which letters of the English alphabet have exactly one line of reflectional symmetry?

Answer: A, B, C, D, E, K, M, T, U, V, W, Y

Question 5

Draw a shape that has exactly two lines of symmetry.

Possible answers: rectangle, rhombus, oval

Shapes with two lines of symmetry

Question 6

Why do you think symmetry is important in design and architecture?

Possible answers: Creates balance and harmony, is pleasing to the eye, makes structures more stable, reflects natural patterns

Ready for more challenges?

Full Practice Set


Symmetry Challenge

Timed Symmetry Test

Test your skills identifying lines of symmetry in various shapes and objects

Identify lines of symmetry in different shapes. Score 80% to advance.