GOAL 1 RELATIONSHIPS BETWEEN LINES

EXAMPLE 1

3.1 LINES AND ANGLES

Vocabulary

•parallel lines—Be sure you understand the notation!

•skew lines

•parallel planes

Extra Example 1

Think of each segment in the diagram as part of a line. Which of the lines appear to fit the description?

a. parallel to and contains V

b. perpendicular to and contains V

c. skew to and contains V

d. Name the plane(s) that contain V and appear to be parallel to plane TPQ.

TW�������������� �

TW�������������� �

TW�������������� �

V

UV�������������� �

WV�������������� �

or RV SV���������������������������������������� ���

plane VRS

Parallel PostulateIf there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.

Perpendicular PostulateIf there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.

PARALLEL AND PERPENDICULAR POSULATES

A Perpendicular to a LineConstruction

Work through the construction activity on page 130.

Checkpoint

Think of each segment in the diagram as part of a line. Which of the lines appear to fit the description?

1. parallel to and contains HJN�������������� �

2. perpendicular to and contains HJN�������������� �

3. skew to and contains HJN�������������� �

4. Name the plane(s) that contain H and appear to be parallel to plane LMN.

HM�������������� �

JH�������������� �

, GH KH���������������������������������������� ���

plane GHJ

Vocabulary

•transversal

•corresponding angles

•alternate exterior angles

•alternate interior angles

•consecutive interior angles (same side interior angles)

GOAL 2 IDENTIFYING ANGLES FORMED BY TRANSVERSALS

3.1 LINES AND ANGLES

EXAMPLE 2

Extra Example 2

List all pairs of angles that fit thedescription.a. corresponding

b. alternate exterior

c. alternate interior

d. consecutive interior

1 and 3; 2 and 4;

5 and 7; 6 and 8

1 and 8; 5 and 4

2 and 7; 3 and 6

2 and 3; 6 and 7

EXAMPLE 3

CheckpointList all pairs of angles that fit the description.

1 23 4

5 67 8

1. corresponding

2. alternate exterior

3. alternate interior

4. consecutive interior

1 and 3, 2 and 4,

5 and 7, 6 and 8

1 and 8, 4 and 5

2 and 7, 3 and 6

6 and 7, 2 and 3

QUESTIONS?

homework

• Pg 132 #1-26