Parallel Lines and Transversals . Angles and parallel lines.

Parallel Lines and Transversals.Angles and parallel lines.

Lesson Objective

Explore relationships of the angles formed by a transversal cutting parallel lines.

VocabularyParallel lines, parallel planes, transversal, consecutive interior angels, alternative exterior angels, alternative interior angels, corresponding

angels.

Video

Parallel Lines: Coplanar lines that do not intersect.

s

cdl

wx

l

x

Name all segments that are parallel to

Answer:

A B

C

E

F G

H

D

Use the figure to name each of the following.

Answer: plane XYZ

Answer:

Answer:

Answer:

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

mtransversalk

214 3

765

8

NAME ANGLES

Exterior angles

Interior anglesConsecutive interior angles

Alternate exterior anglesAlternate interior anglesCorresponding angles

13

2 7 8

4 6 5

6 3 4 5 1 2 7 8

3 5 4 6

1 5 2 6 3 7 4 8

m k

Corresponding Angles Postulate

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

m

k

21

43

765

8

m k

1

3

2

4

6

5

7

8 @ @ @ @

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

….each pair of alternative interior angles is congruent.

21

43

765

8

3 6 @ 4 5 @….each pair of alternative exterior angles is congruent. 1 2 7 8 @ @….each pair of consecutive interior angles issupplementary.m4+ m6=180

m3+ m5=180

geogebra

Answer:

Corresponding Angles PostulateVertical Angles Theorem

Transitive PropertyDefinition of congruent angles

Substitution

In the figure and

Find

Answer:

In the figure and Find

Grid-In Test ItemWhat is the measure of RTV?

Read the Test Item

Be sure to identify it correctly on the figure.

Use an auxiliary line.

Solve the Test Item

Alternate Interior Angles Theorem

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.

Definition of congruent angles Substitution

Alternate Interior AnglesTheorem

Answer:

Grid-In Test ItemWhat is the measure of IGE? Answer:

J

K

If and

find x and y.

Find x.

by the Corresponding Angles Postulate.

ALGEBRA

Definition of congruent angles

Substitution

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

Definition of congruent anglesSubstitution

Find y.

by the Alternate Exterior Angles Theorem.

Simplify.

Add 100 to each side.

Divide each side by 4.

Answer:

Answer:

ALGEBRA If andfind x and y.