Topic 8 Transformational Geometry 84 Symmetry Pearson Texas Geometry 2016 Holt Geometry Texas 2007 TEKS Focus 3D Identify and distinguish between reflectional and rotational symmetry in a plane figure ID: 556705
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Slide1
Pearson Unit 2
Topic
8: Transformational
Geometry
8-4: Symmetry
Pearson Texas Geometry ©2016
Holt Geometry Texas ©2007
Slide2
TEKS
Focus:
(3)(D) Identify and distinguish between
reflectional
and rotational symmetry in a plane figure
.
(1)(C) Select tools, including real objects, manipulatives paper and pencil, and technology as appropriate, and techniques, including mental math, estimations, and number sense as appropriate, to solve problems.
(1)(D) Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
.
(
1)(E) Create and use representations to organize, record, and communicate mathematical ideas
.Slide3Slide4
Which capital letters have horizontal line symmetry?
B C D E H I K O X
Which capital letters have vertical line symmetry?
A H I M O T U V W X Y
Example #
1LINE SYMMETRYSlide5
How many lines of symmetry do regular polygons have? Write a rule using
n
as the number of sides in the polygon.
Example #2
MORE LINE SYMMETRY
7
lines
8
lines
10
lines
A regular polygon with
n
sides has
n
lines of symmetry.Slide6
Do the following figures have rotational symmetry? If yes, then state the degree of the angle of rotation. Assume the point of rotation is the center of the figure.
Example #3
ROTATIONAL SYMMETRY
N
o
N
o
Yes; 180
Yes; 360/7
Yes; 180
Yes; 72
Slide7
Determine if these figures appear to have
reflectional
symmetry,
rotational symmetry (with degree), neither, or both.Example
#
4
Both kinds:
8 lines of reflection
a
nd 45
of rotational
s
ymmetry.
Only 1 line of vertical
reflection.
No symmetry.Slide8
Graph the following parabolas and determine the equation of the line of symmetry:
and
Also determine what makes the parabola move to the left or right of the origin.
Example #5
Graphing Parabolas
Line of symmetry
i
s x = -3
Line of symmetry
i
s x = 1
The
h
in the vertex form controls the horizontal shift.
The
k
in the vertex form controls the vertical shift.