Parallel Lines and Transversals . Angles and parallel lines.

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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

Answer:

H

E

B

A

F

G

D

C

Answer:

Answer:

Answer:

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

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

….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

m4+

m6=180

6

5

m3+

m5=180

7

8

In the figure and

Find

Corresponding Angles Postulate

Vertical Angles Theorem

Transitive Property

Definition of congruent angles

Substitution

Answer:

In the figure and Find

Answer:

Be sure to identify it correctly on the figure.

Use an auxiliary line.

Grid-In Test ItemWhat is the measure of RTV?

Read the Test Item

Solve the Test Item

Alternate Interior Angles Theorem

Definition of congruent angles

Substitution

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.

Answer:

Answer:

Grid-In Test ItemWhat is the measure ofIGE?

K

J

If

and

find x and y.

by the Corresponding Angles Postulate.

ALGEBRA

Find x.

by the Alternate Exterior Angles Theorem.

Definition of congruent angles

Substitution

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

Find y.

Definition of congruent angles

Substitution

Simplify.

Add 100 to each side.

Divide each side by 4.

Answer:

and

ALGEBRA

If

find x and y.

Answer: