12.1: Reflection Symmetry
What if you were asked to consider the presence of symmetry in nature? The starfish, below, is one example of symmetry in nature. Draw in the line(s) of symmetry. After completing this Concept, you'll be able to draw lines of symmetry through shapes and objects like this one.
Watch This
CK-12 Foundation: Chapter12ReflectionSymmetryA
Learn more about reflectional symmetry by watching the video at this link.
Guidance
A line of symmetry is a line that passes through a figure such that it splits the figure into two congruent halves. Many figures have a line of symmetry, but some do not have any lines of symmetry. Figures can also have more than one line of symmetry. A shape has reflection symmetry when it has one or more lines of symmetry.
Example A
Find all lines of symmetry for the shape below.
This figure has two lines of symmetry.
Example B
Does the figure below have reflection symmetry?
Yes, this figure has reflection symmetry.
Example C
Does the figure below have reflection symmetry?
Yes, this figure has reflection symmetry.
Watch this video for help with the Examples above.
CK-12 Foundation: Chapter12ReflectionSymmetryB
Concept Problem Revisited
The starfish has 5 lines of symmetry.
Vocabulary
A line of symmetry is a line that passes through a figure such that it splits the figure into two congruent halves. Reflection symmetry is present when a figure has one or more lines of symmetry.
Guided Practice
Find all lines of symmetry for the shapes below.
1.
2.
3.
Answers:
For each figure, draw lines through the figure so that the lines perfectly cut the figure in half. Figure 1 has eight, 2 has no lines of symmetry, and 3 has one.
1.
2.
3.
Practice
For #1 through #8, determine whether each statement is true or false.
- All right triangles have line symmetry.
- All isosceles triangles have line symmetry.
- Every rectangle has line symmetry.
- Every rectangle has exactly two lines of symmetry.
- Every parallelogram has line symmetry.
- Every square has exactly two lines of symmetry.
- Every regular polygon has three lines of symmetry.
- Every sector of a circle has a line of symmetry.
- What type of shape has an infinite number of lines of symmetry?
Find all lines of symmetry for the letters below.
Determine if the words below have reflection symmetry.
- OHIO
- MOW
- WOW
- KICK
- pod
Trace each figure and then draw in all lines of symmetry.
Determine if the figures below have reflection symmetry. Identify all lines of symmetry.
Congruent
Congruent figures are identical in size, shape and measure.Isosceles Triangle
An isosceles triangle is a triangle in which exactly two sides are the same length.Line of Symmetry
A line of symmetry is a line that can be drawn to divide a figure into equal halves.Line Symmetry
A figure has line symmetry or reflection symmetry when it can be divided into equal halves that match.reflection symmetry
A figure has reflection symmetry if it can be reflected across a line and look exactly the same as it did before the reflection.Symmetry
A figure has symmetry if it can be transformed and still look the same.Image Attributions
Here you'll learn how to determine whether or not a shape has reflection symmetry and how to draw lines of symmetry.
Concept Nodes:
Congruent
Congruent figures are identical in size, shape and measure.Isosceles Triangle
An isosceles triangle is a triangle in which exactly two sides are the same length.Line of Symmetry
A line of symmetry is a line that can be drawn to divide a figure into equal halves.Line Symmetry
A figure has line symmetry or reflection symmetry when it can be divided into equal halves that match.reflection symmetry
A figure has reflection symmetry if it can be reflected across a line and look exactly the same as it did before the reflection.Symmetry
A figure has symmetry if it can be transformed and still look the same.