• Study Resource
• Explore

Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Line (geometry) wikipedia, lookup

Euclidean geometry wikipedia, lookup

Pythagorean theorem wikipedia, lookup

Rational trigonometry wikipedia, lookup

Integer triangle wikipedia, lookup

Trigonometric functions wikipedia, lookup

Multilateration wikipedia, lookup

History of trigonometry wikipedia, lookup

Euler angles wikipedia, lookup

Perceived visual angle wikipedia, lookup

Rotation matrix wikipedia, lookup

Rotation formalisms in three dimensions wikipedia, lookup

Plane of rotation wikipedia, lookup

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
*
2 1 s
B
A
angles 1 and 2 are adjacent
2
6
1
-
complementary angles
two angles whose
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
angles 1 and 2 are
supplementary
2
supplementary
angles do not
need to be adjacent to each
other
1
4
vertical angles
two
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
```
Related documents