Name: ______Date: ______Period: _____
Chapter 4: Transformations Topic 10: Symmetry
There are three types of symmetry that we will consider.
#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 needs to be able to be divided into two “mirror image halves.” The line of symmetry is ______from all corresponding pairs of points.
Another way to think about line symmetry: If the image is reflected of the line of symmetry, it will return the same image.
Examples: In the figures below, sketch all the lines of symmetry (if any): Think critically: Some have one, some have many, some have none! Remember, if the image is reflected over the line you draw, it should be identical to how it started!
More Examples: Letters and numbers can also have lines of symmetry! Sketch as many lines of symmetry as you can (if any):
Name: ______Date: ______Period: _____
#2 Rotational Symmetry:
RECALL! The total measure of degrees around a point is: ______
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. If a polygon is not regular, it may have fewer rotational symmetries. We can consider increments of like coordinate plane rotations.
Examples of Regular Polygons:
A rotation of will always map a figure back onto itself.
This is called the ______.
Determine if the following figures have Rotational Symmetry and the angle of rotation Think back to how we handled rotation transformations… spin your page to help you!
Name: ______Date: ______Period: _____
#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.
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: ______Date: ______Period: _____
Topic 10 Homework: Symmetry
Directions: Answer the following questions completely. Make sure to show all work when you can.
1) Which figure has one and only one line of symmetry? (Sketching will help!) (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)
Name: ______Date: ______Period: _____
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 2) No lines of symmetry about the diagonals.