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Transcript
Geometry: Lines, line segments, rays, and angles
1
Notation and vocabulary for naming lines, line
segments, and rays
term
diagram
s s s ABC
line
s
line segment A
s
A
ray
2
notation
↔
notes
↔
AB or BA
ok to use any pair of
points but not all 3
s
B AB or BA
s
B
→
-
AB
Angles
• formally: union of 2 rays with a common endpoint, called vertex
• more dynamic description of an angle: measurement of rotation
naming angles:
Name
picture
angle A
A
-
1
angle 1
Is
D@
@
BAC
C
s
@s
A
s
B
measuring angles
1
1
• unit: degree = 360
rotation; also minutes ( 60
of a degree) and seconds
1
1
( 60 ) of a minute or 3600 of a degree)
• tool: protractor
• size of an angle is determined by its measure, not by how long the
rays are drawn
1
3
Classifying angles
Name
Definition
right angle
an angle whose measure is 90◦
acute angle
Picture
6
-
*
-
an angle whose measure is between 0◦ and 90◦
I
@
@
obtuse angle
an angle whose measure is between 90◦ and 180◦
@
-
AB(C
straight angle
an angle whose measure is 180◦
s
A
s
B
s C
-
reflex angle
an angle whose measure is between 180◦ and 360◦
Note: It’s good to be familliar with the following angles. We can compare
their size to that of a given angle in order to make reasonable estimates
of the measure of the given angle.
30◦
45◦
2
60◦
4
Relationships between angles
Name
Definition
Picture
Notes
C
s
angles with the same
vertex, a common
side, and disjoint
interiors
adjacent angles
*
2 1 s
B
A
angles 1 and 2 are adjacent
2
6
1
-
complementary angles
two angles whose
measures add to 90◦
angles 1 and 2 are
complementary
ABC is not
adjacent to either angle 1 or
angle 2
complementary
angles do not
need to be adjacent to each
other
2
s
1
-
supplementary angles
two angles whose
measures add to 180◦
angles 1 and 2 are
supplementary
2
supplementary
angles do not
need to be adjacent to each
other
1
4
vertical angles
two
non-adjacent
angles formed when
two lines intersect
3
angles 1 and 3 are
vertical angles and
angles 2 and 4 are
vertical angles
vertical angles
are congruent
(defined below)
Important vocubulary and notation
When two angles have the same measure, we say they are congruent (not equal).
Notation:
6
∼
1=6 2
We can also say their measures are equal.
Notation:
3 m6 1 = m6 2