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Parallel Lines and Transversals . Angles and parallel lines.  Video. Lesson Objective. Explore relationships of the angles formed by a transversal cutting parallel lines. Vocabulary

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Parallel Lines and Transversals . Angles and parallel lines.

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Parallel Lines and Transversals.

Angles and parallel lines.

Video

Lesson Objective

Explorerelationships of the angles formed by a transversal cutting parallel lines.

Vocabulary

Parallel lines, parallel planes, transversal, consecutive interior angels, alternative exterior angels, alternative interior angels, corresponding angels.

Parallel Lines: Coplanar lines that do not intersect.

l

d

c

x

s

w

x

l

Name all segments that are parallel to

H

E

B

A

F

G

D

C

### Example 1-1e

Use the figure to name each of the following.

Transversal: A line that intersects two or

more lines in a plane at different points.

Transversal

crossing

two lines

This transversal

crosses two

parallel lines

This transversal

cut across three

lines

Transversal and angles

m

k

transversal

m

1

2

4

3

k

5

6

8

7

1

2

7

8

3

4

5

6

3

6

4

5

1

7

2

8

3

5

4

6

1

5

2

6

3

7

4

8

### Corresponding Angles Postulate

If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.

m

k

@

m

5

1

1

2

@

3

7

3

4

k

6

@

5

2

6

7

8

@

4

8

### When two parallel lines are cut by a transversal, then….

….each pair of alternative interior angles is congruent.

@

@

3

6

4

5

….each pair of alternative exterior angles is congruent.

geogebra

@

@

1

8

2

7

….each pair of consecutive

interior angles is

supplementary.

1

2

3

4

m4+

m6=180

6

5

m3+

m5=180

7

8

In the figure and

Find

### Example 2-1a

Corresponding Angles Postulate

Vertical Angles Theorem

Transitive Property

Definition of congruent angles

Substitution

In the figure and Find

### Example 2-1b

Be sure to identify it correctly on the figure.

Use an auxiliary line.

### Example 2-2a

Grid-In Test ItemWhat is the measure of RTV?

### Example 2-2b

Solve the Test Item

Alternate Interior Angles Theorem

Definition of congruent angles

Substitution

### Example 2-2c

Alternate Interior AnglesTheorem

Definition of congruent angles

Substitution

Write each digit of 125 in a column of the grid. Then shade in the corresponding bubble in each column.

### Example 2-2d

Grid-In Test ItemWhat is the measure ofIGE?

K

J

If

and

find x and y.

by the Corresponding Angles Postulate.

### Example 2-3e

ALGEBRA

Find x.

by the Alternate Exterior Angles Theorem.

### Example 2-3f

Definition of congruent angles

Substitution

Subtract x from each side and add 10 to each side.

Find y.

Definition of congruent angles

Substitution

### Example 2-3g

Simplify.

Divide each side by 4.