Line and Angle Relationships

Sec 6.1

GOALS:To learn vocabularyTo identify angles and relationships of angles formed by tow parallel lines cut by a transversal

l BA

or ABl$%%%%%%%%%%%%% %

Line

Ray

Angle

A B

AB%%%%%%%%%%%%%%

A

BC

ABC or B sidesvertex

Vocabulary

Types of Angles Acute angles – angles that have measures between 0

and

Right angles – angles that have measures equal to

Obtuse angles – angles that have measures between

Straight angles – angles that have measures equal to

90

90

90 180and

180

Special Pairs of Angles Vertical angles – opposite angles formed by

intersecting lines. Vertical angles are congruent.

41

2

3

1 2and are vertical angles

1 2

Special Pairs of Angles Adjacent angles – angles that have the same vertex,

share a common side, and do not overlap.

21

1 2 are adjacent anglesand

A

BC

1 2m ABC m m

Special Pairs of Angles Complementary angles – angles whose sum is 90

40

A

BC

D50

m ABC m ABD m DBC

50 40 90m ABC

and are commplementary anglesABD DBC

Special Pairs of Angles Supplementary angles – angles whose sum is 180

40 A B

140

180m A m B

and are supplementary anglesA B

Examples

Perpendicular Lines Perpendicular lines – lines that intersect at right

angles

k h

k

h

Parallel Lines Parallel lines – two lines in a plane that never

intersect or cross

k h

k

h

7

Transversal A line that intersects two or more other lines is called a

transversal. Eight angles are formed when a transversal intersect two lines.

8

4 3

6 5

2 1

t

7

Corresponding Angles Postulate

Corresponding angles are those in the same position on the two lines in relation to the transversal.

If two parallel lines are cut by a transversal, then corresponding angles are congruent.

8

4 3

6 5

2 1

1 5

2 6

3 7

4 8

7

Alternate Interior Angles Theorem

Alternate interior angles are those on opposite sides of the transversal and inside the other two lines.

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

8

4 3

6 5

2 1

4 5

3 6

7

Alternate Exterior Angles Theorem

Alternate exterior angles are those on opposite sides of the transversal and outside the other two lines.

If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.

8

4 3

6 5

2 1

1 8

2 7

ExampleGiven: Find: x

k h

Alternate Exterior Angles Are Congruent

kh

x

72

Example Given: Find: x and the angle measure

k h

Alternate Interior Angles Theorem

k

h

35

x

Example

Given: Find the angles shown.

4

35

2

118°

k h

2 180 118 62

su

m

definition of pplementary angles

5 622 5 m

Alternate Interior Angles Theorem

4 3

Vertical angles are congruent

k

h

2 62 ,2 3 180

3 118

sec

and m

so

Angles

m m

m

Con utive Interior Theorem

Students Given: Find: All other angle measures

k h

3 4 7 30

1 180 30 150 2 5 6

m m m

m m m m

kh

1302

5

3 6 74

Homework Page 259 13-15, 19-22, 30-33, 47-49