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Parallel Lines and Transversals . Angles and parallel lines. PowerPoint PPT Presentation


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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

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 and transversals angles and parallel lines

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


Parallel lines and transversals angles and parallel lines

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


Parallel lines and transversals angles and parallel 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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