Warm-Up Find the measure of all angles possible.

112º

138º

2.1.

2.6 Parallel Line Angles ObjectiveBe able to understand the angles made by

parallel lines.

Special Angles on Parallel Lines

Investigation 1) Angles on Parallel Lines

Step 1) Using a ruler, draw a pair of parallel lines on your paper.

Step 2) Draw a line that intersects both parallel lines (a transversal).

Angles on Parallel Lines

Special Angles on Parallel Lines Step 3) Label the Angles 1-8

1 2

43

5 6

7 8

Special Angles on Parallel Lines Step 4) Place the patty paper over angles 1-4

and trace the intersecting lines and the four angles.

1 2

43

Special Angles on Parallel Lines Step 5) Slide the patty paper down to angles

5-8. What do you notice?

1 2

43

Special Angles on Parallel LinesKeyword Conjecture Sketch

Corresponding Corresponding Angles are ___________.

Angles (CA)

Alternate Interior Alternate Interior angles are __________.

Angles (AIA)

Alternate Exterior Alternate Exterior angles are _________.

Angles (AEA)

congruent

congruent

congruent

43

865

1 2

7

43

865

1 2

7

43

865

1 2

7

Special Angles on Parallel LinesKeyword Conjecture Sketch

Consecutive Interior Same Side Interior AnglesAngles are _______________.

Consecutive Exterior Same side exterior anglesAngles are ______________.

Parallel lines If two parallel lines are cut by a transversal, then Conjecture corresponding angles are ____________, alternate

interior angles are ______________, and alternate exterior angles are ________________.

supplementary

supplementary

43

865

1 2

7

43

865

1 2

7

congruentcongruent

congruent

Special Angles on Parallel Lines If 2 lines are cut by a transversal to form pairs of

congruent Corresponding Angles, congruent Alternate Interior Angles, congruent Alternate Exterior Angles, supplementary Consecutive interior angles, or supplementary exterior angles, then the lines are ________________.

Converse of Parallel Lines Conjecture

parallel

Conversel m

n

p

1 2

3 4

5 67 8

9 1011 12

13 14

16 15

Summary Name four sets of angles formed by two

parallel lines cut by a transversal Name one set of supplementary angles

formed by two parallel lines cut by a transversal.

Classwork: page 130 #7 copy the picture

q

a

c

169

64

ks

d

108

gh

j

i

fe

b

61t

75m

n

p79

Homework Pg 129 #1-3, 9-15 Pg. 140 #26