9.1 – Points, Line, Planes and Angles
Definitions:
A point has no magnitude and no size.
A line has no thickness and no width and it extends
indefinitely in two directions.
A plane is a flat surface that extends infinitely.
m
A
D

E
9.1 – Points, Line, Planes and Angles
Definitions:
A point divides a line into two half-lines, one on each side of
the point.
A ray is a half-line including an initial point.
A line segment includes two endpoints.
N
E
D

F
G
9.1 – Points, Line, Planes and Angles
Summary:
Name
Figure
Line AB or BA
Half-line AB
Ray AB
A
A
A
BA
B
AB
B
A
BA
AB
B
A
Ray BA
Segment AB or
Segment BA
AB
B
A
Half-line BA
Symbol
BA
B
B
AB
BA
9.1 – Points, Line, Planes and Angles
Definitions:
Parallel lines lie in the same plane and never meet.
Two distinct intersecting lines meet at a point.
Skew lines do not lie in the same plane and do not meet.
Parallel
Intersecting
Skew
9.1 – Points, Line, Planes and Angles
Definitions:
Parallel planes never meet.
Two distinct intersecting planes meet and form a straight line.
Parallel
Intersecting
9.1 – Points, Line, Planes and Angles
Definitions:
An angle is the union of two rays that have a common endpoint.
A
Vertex
B
1
C
An angle can be named using the following methods:
– with the letter marking its vertex, B
– with the number identifying the angle, 1
– with three letters, ABC.
1) the first letter names a point one side;
2) the second names the vertex;
3) the third names a point on the other side.
9.1 – Points, Line, Planes and Angles
Angles are measured by the amount of rotation in degrees.
Classification of an angle is based on the degree measure.
Measure
Name
Between 0° and 90°
Acute Angle
90°
Right Angle
Greater than 90° but less
than 180°
180°
Obtuse Angle
Straight Angle
9.1 – Points, Line, Planes and Angles
When two lines intersect to form right
angles they are called perpendicular.
Vertical angles are formed when two lines intersect.
A
D
B
E
C
ABC and DBE are one pair of vertical angles.
DBA and EBC are the other pair of vertical angles.
Vertical angles have equal measures.
9.1 – Points, Line, Planes and Angles
Complementary Angles and Supplementary Angles
If the sum of the measures of two acute angles is 90°, the
angles are said to be complementary.
Each is called the complement of the other.
Example: 50° and 40° are complementary angles.
If the sum of the measures of two angles is 180°, the angles
are said to be supplementary.
Each is called the supplement of the other.
Example: 50° and 130° are supplementary angles
9.1 – Points, Line, Planes and Angles
Find the measure of each marked angle below.
(5x – 10)°
(3x + 10)°
Vertical angels are equal.
3x + 10 = 5x – 10
2x = 20
x = 10
Each angle is 3(10) + 10 = 40°.
9.1 – Points, Line, Planes and Angles
Find the measure of each marked angle below.
(2x + 45)°
(x – 15)°
Supplementary angles.
2x + 45 + x – 15 = 180
3x + 30 = 180
3x = 150
x = 50
2(50) + 45 = 145
50 – 15 = 35
35° + 145° = 180
9.1 – Points, Line, Planes and Angles
1
Parallel Lines cut by a Transversal
line create 8 angles
5
4
3
5 6
7 8
Alternate interior angles
Angle measures are equal.
(also 3 and 6)
1
Alternate exterior angles
Angle measures are equal.
8
(also 2 and 7)
2
4
9.1 – Points, Line, Planes and Angles
1
2
3 4
5 6
7 8
Same Side Interior angles
Angle measures add to 180°.
4
6
(also 3 and 5)
2
Corresponding angles
6
Angle measures are equal.
(also 1 and 5, 3 and 7, 4 and 8)
9.1 – Points, Line, Planes and Angles
Find the measure of each marked angle below.
(3x – 80)°
(x + 70)°
Alternate interior angles.
x + 70 = 3x – 80
2x = 150
x = 75
x + 70 =
75 + 70 =
145°
9.1 – Points, Line, Planes and Angles
Find the measure of each marked angle below.
(4x – 45)°
(2x – 21)°
Same Side Interior angles.
4x – 45 + 2x – 21 = 180
6x – 66 = 180
6x = 246
x = 41
4(41) – 45
2(41) – 21
164 – 45
82 – 21
119°
61°
180 – 119 = 61°