8.6 Polygon Symmetry & Rotational Symmetry Name _____________________________Per. ___
Lines of Symmetry
A line that reflects a figure onto itself is called a line of symmetry (also called line of reflection). A figure that can be
carried onto itself by a rotation is said to have rotational symmetry.
Every four-sided polygon is a quadrilateral. Some quadrilaterals have additional properties and are given special
names like squares, parallelograms and rhombuses. In this task you will use rigid-motion transformations to explore
line symmetry and rotational symmetry in various types of shapes.
1. Draw the lines of symmetry for each regular polygon, fill in the table including an expression for the number
of lines of symmetry in a n-sided polygon. A regular polygon has all sides the same length and all angles are the same
measurement.
Name of Regular Polygon
Number of
Vertices (sides)
Predict number of lines of
reflection and draw them
Determine actual lines of
reflection by folding cut-out
polygons.
Equilateral Triangle
Square
Regular Pentagon
Regular Hexagon
2. What patterns do you notice in terms of the number and characteristics of the lines of reflection in a regular
polygon?
3. How many lines of reflection would be on 952-gon?
4. Is a Circle a regular n-gon? Explain.
5. How many lines of reflection in a circle? Explain
6. Non-regular polygons
Name of Non-Regular Polygon
Rectangle
Isosceles Trapezoid
Parallelogram
Rhombus
Number of
Vertices (sides)
Predict number of lines of
reflection and draw them
Determine actual lines of
reflection by folding cut-out
polygons.
7. What patterns do you notice in terms of the number and characteristics of the lines of reflection in a non-regular
polygon?
8. How many lines of reflection would be on 952-gon?
9. Is it possible to rotate the image onto itself?
Use your cut-out polygons over the top of the matching polygons from the other half of your paper and determine
the degree of rotation needed to carry the polygon onto itself. THERE MAY BE MORE THAN ONE ROTATION
POSSIBLE! List all possibilities up to and including 360⁰.
Name of Regular Polygon
Number of
Vertices (sides)
List all degrees of rotation that will carry the polygon onto
itself up to and including 360⁰
Equilateral Triangle
Square
Regular Pentagon
Regular Hexagon
Name of Non-Regular Polygon
Rectangle
Isosceles Trapezoid
Parallelogram
Rhombus
10. Is there a way to determine the degrees of rotation that will carry a REGULAR POLYGON onto itself?
11. Use what you discovered above for Regular Polygons and determine all the degrees of rotation
that will carry a regular octagon onto itself.
12. Rotate each given point about the origin and state the new coordinates.
A. (−2, 4), 𝑟𝑜𝑡𝑎𝑡𝑒 90° Clockwise A’ =_____________
B. (−3, 4), 𝑟𝑜𝑡𝑎𝑡𝑒 90° Counterclockwise B’ = _____________
C. (5, 2) , 𝑟𝑜𝑡𝑎𝑡𝑒 180° Clockwise
C’ = _____________
D. (1, −8), 𝑟𝑜𝑡𝑎𝑡𝑒 180° Counterclockwise D’ = ____________
31. Reflect the point over the line of
reflection
32. reflect the point over the given
line of reflection
33. Rotate the triangle 90⁰ clockwise
around
the point
(0,-2)
Write the slope-intercept form of the equation for the lines that are parallel and
perpendicular to 𝑦 = 5𝑥 − 5 that goes through (-15,8)
34. Parallel equation
35. Perpendicular equation
Write the slope-intercept form of the equation for the lines that are parallel and
perpendicular to 𝑦 = 2𝑥 − 5 that goes through (-10,8)
36. Parallel equation
37. Perpendicular equation
Given (-3, 10) and (-7, 17) Show your work!
38. Determine the midpoint of the segment
Given (3, 10) and (-7, 20) Show your work!
40. Determine the midpoint of the segment
39. Determine the distance between the
points. Simplify any radical answers if
possible. No decimals.
41. Determine the distance between the
points. Simplify any radical answers if
possible. No decimals.
Key:
10. 360/#sides
11. 45⁰, 90⁰, 135⁰, 180⁰, 225⁰, 270⁰, 315⁰, 360⁰ 12. A’ (4,2) B’(-4,-3) C’(-5,-2) D’(-1,8)
31. (-2,5) 32. (0,0)
36. y=2x+28
33. K’(5,2) L’(3,0) J’(1,2)
1
37. 𝑦 = − 𝑥 + 3
2
38. (-5,13.5)
34. Y=5x+83
39. √65
1
35. 𝑦 = − 5 𝑥 + 5
40. (-2, 15) 41. 10√2