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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.

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


Example 1 1c

Name all segments that are parallel to

Answer:

Example 1-1c

H

E

B

A

F

G

D

C


Example 1 1e

Answer:

Answer:

Answer:

Example 1-1e

Use the figure to name each of the following.

Answer: plane XYZ


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

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
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


Example 2 1a

In the figure and

Find

Example 2-1a

Corresponding Angles Postulate

Vertical Angles Theorem

Transitive Property

Definition of congruent angles

Substitution

Answer:


Example 2 1b

In the figure and Find

Answer:

Example 2-1b


Example 2 2a

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?

Read the Test Item


Example 2 2b
Example 2-2b

Solve the Test Item

Alternate Interior Angles Theorem

Definition of congruent angles

Substitution


Example 2 2c
Example 2-2c

Alternate Interior AnglesTheorem

Definition of congruent angles

Substitution

Angle Addition Postulate

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


Example 2 2c1
Example 2-2c

Answer:


Example 2 2d

Answer:

Example 2-2d

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

K

J


Example 2 3e

If

and

find x and y.

by the Corresponding Angles Postulate.

Example 2-3e

ALGEBRA

Find x.


Example 2 3f

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
Example 2-3g

Simplify.

Add 100 to each side.

Divide each side by 4.

Answer:


Example 2 3h

and

ALGEBRA

If

find x and y.

Example 2-3h

Answer:


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