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Transcript 
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
The word geometry comes from a Greek word meaning 'to measure the earth."
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
Math
Book
p 324
OH Academic content Standards
8.3.2
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
Learning Objective
Students will learn to classify angles and find their measures. Students will demonstrate their understanding through class work.
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
A quick review:
A point names a location.
.A
point A
A line is perfectly straight and extends forever in both directions.
.
A
l
.
B
line l or AB
or BA
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
A plane is a perfectly flat surface that extends forever in all directions. S
T
plane f
f
R
or
Q
plane QRST
.
A segment, or line segment, is the part of a line between two points. .
B
AB or BA
A
A ray is part of a line that starts at one point .
and extends forever in one direction.
B
.
AB
A
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
.
Use the diagram to name each type of figure.
P
1. MP _____________
2. k ______________
.
.
.
k
J
3. MN ______________
N
4. LJ ______________
5. JL ______________
M
.
L
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
An angle ( ) is formed by two rays, or sides, with a common endpoint called the vertex. You can name an angle several ways: by its vertex, by its vertex and a point on each ray, or by a number. When three points are used, the middle point must be the vertex.
Y
XYZ
ZYX
1
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
Types of Angles
Acute Angle
Right Angle
Obtuse Angle Straight Angle
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
07­1 Points, Lines, Planes, and Angles.notebook
BDC
ABC
December 16, 2013
07­1 Points, Lines, Planes, and Angles.notebook
A and B are
complementary angles.
December 16, 2013
C and D are
supplementary angles.
Complementary and Supplementary Angles ­ YouTube.website
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
When two lines intersect they form
four angles. Angles that have the same
vertex and whose sides are opposite rays
are called vertical angles, and they are
always congruent.
m
1=m
3
m
2=m
4
1 2
4 3
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
pairs of vertical angles
a and b
c and d
m 1 = 37o
m 2 =
m 3 =
m 4 =
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
Congruent figures have the same size and shape.
The symbol
≅ means is congruent to.
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
What's the difference between
congruent and equal?
Only numerical measures
(such as the measure of an
angle or the length of a
segment) are called equal.
Figures that are the
same shape and size
are congruent.
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
Complete these statements about congruence.
. .. .
.
.
. .
2
4
4
D
B C
A
Since AC = 6 units and BD = 6 units,
then AC _________ BD.
A
300
300
B
Since m ABC = 30o and m CBD = 30o
then ABC = _________.
C
D
.
.
. .
.
U
S
P
J
V
Since vertical angles are congruent,
then UPJ ___________________.
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
07­1 Points, Lines, Planes, and Angles.notebook
December 16, 2013
Attachments
Complementary and Supplementary Angles ­ YouTube.website
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