Name:________________________________________________________________
Date:__________________________ Period:______
Symmetry
1) Line Symmetry:
A line of symmetry not only cuts a figure in___________________, it creates a mirror image. In order to determine if a
figure has line symmetry, a figure can be divided into two “mirror image halves.” The line of symmetry
is ____________________________from all corresponding pairs of points.
Another way of thinking about line symmetry is that a figure has line symmetry such that the image of the figure
when reflected over the line is itself.
Examples:
In the figures below, sketch all the lines of symmetry (if any):
More Examples:
Letters and numbers can also have lines of symmetry! Sketch as many lines of symmetry as you can (if any):
2) Rotational Symmetry:
A rotational symmetry of a figure is a rotation of the plane that maps the figure back to itself such that the rotation
is greater than
, but less than ___________________.
In regular polygons (polygons in which all sides are congruent), the number of rotational symmetries equals the
number of sides of the figure.
A rotation of
Symmetry)
will always map a figure back onto itself! This is called the Identity Transformation (Identity
Think back to Rotations:
90-turn the paper once
180-turn the paper twice
270-turn the paper three times
360-turn it all the way around
(four times)
Center of Rotation
Determine if the following figures have Rotational Symmetry and/or Identity Symmetry.
3) Point Symmetry:
Point symmetry is when every part of the image has a matching part that is…
·The same distance from the central point.
·In the opposite direction.
When an image has point symmetry, it looks the same from opposite directions, such as left vs. right, or if turned
upside down.
In point symmetry, the center is a ______________________to every segment formed by joining a point to its image.
*A simple check to test to see if a figure has point symmetry is to turn the paper upside-down and see if it looks the
same. If the figure looks the same, it has point symmetry. A figure that has point symmetry is unchanged after a
180-degree rotation.
Let’s notice how these all have Point Symmetry!
Let’s see if these figures have point symmetry! Circle the ones that do.
Examples:
Using regular pentagon ABCDE pictured to the right, complete the following questions:
1) Draw in all lines of symmetry.
2) Locate the center of rotational symmetry. Label this point F.
3) Is there rotational symmetry? If so, how many?
4) How many degrees of rotational symmetry does it have?
5) Does it have point symmetry?
Name:______________________________________________________
Symmetry Homework
Date:________________ Period:__________
Geometry
Directions: Answer the following questions completely. Make sure to show all work.
1) Which figure has one and only one line of symmetry?
(a) rhombus
(b) circle
(c) square
(d) isosceles trapezoid
2) Which type of symmetry, if any, does a square have?
(a) line symmetry, only
(b) both line and point symmetry
(c) point symmetry
(d) no symmetry
3) Which letter has both line and point symmetry?
(a) Z
(b) T
(c) C
(d) H
4) What is the total number of lines of symmetry for an equilateral triangle?
(a) 1
(b) 2
(c) 3
(d) 4
5) Which letter has point symmetry but no line symmetry?
(a) E
(b) S
(c) W
(d) O
6) Which number has both horizontal and vertical line symmetry?
(a) 8I8
(b) 383
(c) 414
(d) 100
7) Which letter has line symmetry but no point symmetry?
(a) O
(b) X
(c) N
(d) M
8) Which geometric shape does not have any lines of symmetry?
(a)
(b)
(c)
(d)
9) Using regular octagon pictured to the right, complete the following questions:
a) Draw in all lines of symmetry.
b) Locate the center of rotational symmetry. Label this point F.
c) Is there rotational symmetry? If so, how many?
d) How many degrees of rotational symmetry does it have?
e) Does it have point symmetry?
10) Using the diagram pictured to the right, complete the following questions:
a) Draw in all lines of symmetry.
b) Locate the center of rotational symmetry. Label this point I.
c) Is there rotational symmetry? If so, how many?
d) How many degrees of rotational symmetry does it have?
e) Does it have point symmetry?
11) Using the figure provided, shade exactly 2 of the 9 smaller squares so that the resulting figure has:
1) Only two lines of symmetry
about the diagonals.
2) No lines of symmetry