1. 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 E D

2. 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 G F

3. 9.1 – Points, Line, Planes and Angles
Summary:
Name
Figure
Symbol
Line AB or BA A B AB BA
Half-line AB A B AB
Half-line BA A B BA
Ray AB A B AB
Ray BA A B BA
Segment AB or Segment BA A B AB BA

4. 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

5. 9.1 – Points, Line, Planes and Angles
Definitions:
Parallel planes never meet.
Two distinct intersecting planes meet and form a straight line.
Parallel
Intersecting

6. 9.1 – Points, Line, Planes and Angles
Definitions:
An angle is the union of two rays that have a common endpoint. A
Side
Vertex B 1
Side 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.

7. 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°
Obtuse Angle
180°
Straight Angle

8. 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. 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

10. 9.1 – Points, Line, Planes and Angles
Find the measure of each marked angle below.
(3x + 10)°
(5x – 10)°
Vertical angels are equal.
3x + 10 = 5x – 10
2x = 20
x = 10
Each angle is 3(10) + 10 = 40°.

11. 9.1 – Points, Line, Planes and Angles
Find the measure of each marked angle below.
(2x + 45)°
(x – 15)°
Supplementary angles.
2x x – 15 = 180
3x + 30 = 180
3x = 150
x = 50
2(50) + 45 = 145
50 – 15 = 35
35° + 145° = 180

12. 9.1 – Points, Line, Planes and Angles
1 2
Parallel Lines cut by a Transversal line create 8 angles
3 4
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)

13. 9.1 – Points, Line, Planes and Angles
1 2
3 4
5 6
7 8
Same Side Interior angles 4 6
Angle measures add to 180°.
(also 3 and 5) 2
Corresponding angles 6
Angle measures are equal.
(also 1 and 5, 3 and 7, 4 and 8)

14. 9.1 – Points, Line, Planes and Angles
Find the measure of each marked angle below.
(3x – 80)°
(x + 70)°
Alternate interior angles.
x + 70 =
x = 3x – 80 =
2x = 150
145°
x = 75

15. 9.1 – Points, Line, Planes and Angles
Find the measure of each marked angle below.
(4x – 45)°
(2x – 21)°
Same Side Interior angles.
4x – x – 21 = 180
4(41) – 45
2(41) – 21
6x – 66 = 180
164 – 45
82 – 21
6x = 246
119°
61°
x = 41
180 – 119 = 61°