What if you you had a six-pointed star, you drew a line down it, and then you folded it along that line? If the two sides of the star lined up, what would that mean about the line? After completing this Concept, you'll be able to draw the lines of symmetry for a figure like this one.
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Guidance
A line of symmetry is a line that passes through a figure such that it splits the figure into two congruent halves such that if one half were folded across the line of symmetry it would land directly on top of the other half.
Reflection symmetry is present when a figure has one or more lines of symmetry. These figures have reflection symmetry:
These figures do not have reflection 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.
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
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.
Draw the following figures.
- A quadrilateral that has two pairs of congruent sides and exactly one line of symmetry.
- A figure with infinitely many 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.