Transcript Geometry warm up

Geometry warm up
D is the midpoint of AC
Name a ray that bisects AC
B
DB
E
30°
Name the bisector of <CDB
DF
or DF
45°
A
BD
Name the perpendicular
bisector of AC
or BD
BD
F
60°
D
or
45°
C
When you get done with this,
please make a new note book
3.1 Symmetry in Polygons
What is symmetry?
There are two types we’re concerned with:
Rotational and Reflective
♥If a figure has ROTATIONAL symmetry, then you can rotate it
about a center and it will match itself (don’t consider 0° or 360°)
♥If a figure has REFLECTIONAL symmetry, it will reflect across
an axis.
What are polygons?
♥A plane figure formed by 3 or more segments
♥Has straight sides
♥Sides intersect at vertices
♥Only 2 sides intersect at any vertex
♥It is a closed figure
Names of polygons
• Polygons are named
by the number of
sides they have:
Polygon
Sides
Triangle
3
Quadrilateral
4
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
Nonagon
9
Decagon
10
11-gon
11
Dodecagon
12
13-gon
13
N-gon
n
Vocabulary
• Equiangular – All angles are congruent
• Equilateral – All sides are congruent
• Regular (polygon) – All angles have the same
measure AND all sides are congruent
• Reflectional Symmetry – A figure can be cut in
half and reflected across an axis of symmetry.
• Rotational Symmetry – A figure has rotational
symmetry iff it has at least one rotational image
(not 0° or 360°) that coincides with the original
image.
A little more vocab
♥ EQUILATERAL triangle
has 3 congruent sides
♥ ISOCELES triangle has
at least 2 congruent sides
♥ SCALENE triangle has 0
congruent sides
♥ Center – in a regular
polygon, this is the point
equidistant from all
vertices
♥ Central Angle – An angle
whose vertex is the
center of the polygon
center
C
Central
angle
Activities
♥ 3.1 Activities 1- 2 (hand out)
♥ Turn it in with your homework
What you should have learned
about Reflectional symmetry in
regular polygons
♥ When the number of sides is even, the axis of symmetry
goes through 2 vertices
♥ When the number of sides is odd, the axis of symmetry
goes through one vertex and is a perpendicular bisector
on the opposite side
What you should have learned
about rotational symmetry
♥ To find the measure of the central angle, theta,
θ, of a regular polygon, divide 360° by the
number of sides. 360/n = theta
♥ To find the measure of theta in other shapes,
ask: “when I rotate the shape, how many times
does it land on top of the original?”
♥ Something with 180° symmetry would have 2-fold
rotational symmetry
♥ Something with 90 degree rotational symmetry would
be 4-fold
Homework
♥ Practice 3.1 A, B & C worksheets