December 10, 2014
Reflection-Symmetric Figures
A plane figure F is a reflection-symmetric figure if and only if there
is a line m such that rm(F) = F. The line m is a symmetry line for the
figure.
Flip-Flop Theorem
1. If F and G are points and rl(F) = G, then rl(G) = F.
2. If F and G are figures and rl(F) = G, then rl(G) = F.
Segment Symmetry Theorem
Every segment has exactly two symmetry lines:
1 - its perpendicular bisector
2- the line containing the segment.
Side-Switching Theorem
If one side of an angle is reflected over the line containing the angle
bisector, its image is the other side of the angle.
Angle Symmetry Theorem
The line containing the bisector of an angle is a symmetry line of the
angle.
Circle Symmetry Theorem
A circle is reflection-symmetric to any line through its center.
Symmetric Figures Theorem
If a figure is symmetric, then any pair of corresponding parts under the
symmetry are congruent.
December 10, 2014
Reflection-Symmetric Logos
December 10, 2014
Examples
1. a. How many symmetry lines does a line have?
b. Describe them.
2. Line m is a symmetry line for figure PQRS. What can be deduced
using the Symmetric Figures Theorem?
m
P
Q
R
S
3. Draw all lines of symmetry.
a. equilateral triangle
b. hexagon
c. pentagram
December 10, 2014
Assignment: p. 304 (2-12 even, 16-22 even)