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.

9.1 – Points, Line, Planes and AnglesDefinitions:

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.

A

DE

m

9.1 – Points, Line, Planes and AnglesDefinitions: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.

D

E

N

F

G

Name Figure Symbol

9.1 – Points, Line, Planes and Angles

Summary:

A B AB BA

AB

BA

AB

BA

A B

A B

Line AB or BA

Half-line AB

Half-line BA

Ray AB

Ray BA

Segment AB or Segment BA

A B

A B

A B AB BA

9.1 – Points, Line, Planes and AnglesDefinitions:

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 AnglesDefinitions:Parallel planes never meet.

Parallel Intersecting

Two distinct intersecting planes meet and form a straight line.

9.1 – Points, Line, Planes and AnglesDefinitions:An angle is the union of two rays that have a common endpoint.

Vertex BSide

Side

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.

C

A

1

9.1 – Points, Line, Planes and AnglesAngles are measured by the amount of rotation in degrees.

Classification of an angle is based on the degree measure.

Measure NameBetween 0° and 90° Acute Angle

90° Right Angle

Greater than 90° but less than 180°

Obtuse Angle

180° Straight Angle

9.1 – Points, Line, Planes and AnglesWhen two lines intersect to form right angles they are called perpendicular.

Vertical angles are formed when two lines intersect.A

CB

D

E

Vertical angles have equal measures.

ABC and DBE are one pair of vertical angles.

DBA and EBC are the other pair of vertical angles.

9.1 – Points, Line, Planes and AnglesComplementary 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 AnglesFind the measure of each marked angle below.

(3x + 10)° (5x – 10)°

3x + 10 = 5x – 10

Each angle is 3(10) + 10 = 40°.

Vertical angels are equal.

2x = 20

x = 10

9.1 – Points, Line, Planes and AnglesFind the measure of each marked angle below.

(2x + 45)° (x – 15)°

2x + 45 + x – 15 = 180

35° + 145° = 180

Supplementary angles.

3x + 30 = 180

3x = 150

x = 50

2(50) + 45 = 14550 – 15 = 35

9.1 – Points, Line, Planes and Angles

1 23 4

5 67 8

Alternate interior angles

Alternate exterior angles

Angle measures are equal.

Angle measures are equal.

1

5 4

8

(also 3 and 6)

(also 2 and 7)

Parallel Lines cut by a Transversal line create 8 angles

9.1 – Points, Line, Planes and Angles

1 23 4

5 67 8

Same Side Interior angles

Corresponding angles

Angle measures are equal.

Angle measures add to 180°.4

6

2

6

(also 3 and 5)

(also 1 and 5, 3 and 7, 4 and 8)

9.1 – Points, Line, Planes and AnglesFind the measure of each marked angle below.

(x + 70)°(3x – 80)°

Alternate interior angles.

x + 70 = 3x – 80

2x = 150

x = 75 145°

x + 70 =

75 + 70 =

9.1 – Points, Line, Planes and AnglesFind the measure of each marked angle below.

(2x – 21)°

(4x – 45)°

Same Side Interior angles.

4x – 45 + 2x – 21 = 180

6x – 66 = 180

6x = 246 119°

4(41) – 45

164 – 45

x = 41

180 – 119 = 61°

61°

2(41) – 21

82 – 21