**Parallel Lines and Transversals**

transversals

- A line, ray, or segment that intersects two or more coplanar lines, rays, or segments, each at a different point.

transversals

Properties of parallel lines with transversals

Interior angles

1

2

3

4

Angles:

angle 1 = angle 4

angle 2 = angle 3

angles 1 and 2 are supp.

angles 3 and 4 are supp.

angles 3 and 1 are supp.

angles 4 and 2 are supp.

Exterior angles

1

2

3

4

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Angles:

angle 1 = angle 4

angle 2 = angle 3

angles 1 and 2 are supp.

angles 3 and 4 are supp.

angles 3 and 1 are supp.

angles 4 and 2 are supp.

All angles

1

2

3

4

5

6

7

8

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Angles:

angle 1 = angle 4 = angle 5 = angle 8

angle 2 = angle 3 = angle 6 = angle 7

Supplementary angles

angles 1 and 2, 3 and 4, 5 and 6, 7 and 8,

7 and 5, 8 and 6, 3 and 1, 4 and 2, 1 and 5,

2 and 6, 7 and 3, 8 and 4, 8 and 2, 1 and 7

**Oreos!**

You have an oreo, you are also very bored. You decide to cut it and measure all the angles. But after measuring the first angle, which was 66 , your protractor breaks. Don't ask how... Find all the other angles.

**Oreos! continued.**

66

o

2

3

4

5

6

7

8

**Hint:**

o

The Theorems

You have just used three theroms without even knowing you used them.

Alternate interior angles Theorem

If two lines cut by a transversal are parallel, then alternate interior angles are congruent.

Alternate exterior angles Theorem

If two lines cut by a transversal are parallel, then alternate exterior angles are congruent.

Same-side interior angles Theorem

If two lines cut by a transversal are parallel, then same-side interior angles are supp.

Now try this!

Open your book to page 160 and do #22-27.

A

B

C

D

E

80

25

50

o

o

o

**DONE!**

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**Listen to the teachers on whether or not to take notes.**

corresponding angles

1

2

3

4

5

6

7

8

Angles:

angles 1 = angle 5

angles 2 = angle 6

angles 7 = angle 3

angles 8 = angle 4

Corresponding angles postulate

If two lines cut by a transversal are parallel, then corresponding angles are congruent.

1

5

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3

6

1

8

3

5