C-3 Determining if lines are parallel

✓ If two lines cut by a transversal are _________________________ then,

o alternate interior angles ___________________

o alternate exterior angles ___________________

o corresponding angles ___________________

o consecutive (same side) interior angles ___________________

For example:

What if we went BACKWARDS?

The 4 Ways to prove lines are parallel

✓ Corresponding Angles Converse:

If corresponding angles are __________________, then the lines are __________________.

Example:

Non Example:

✓ Alternate Interior Angles Converse:

If alternate interior angles are __________________, then the lines are __________________.

Example:

Non Example:

✓ Alternate Exterior Angles Converse:

If alternate exterior angles are __________________, then the lines are __________________.

Example:

Non Example:

✓ Consecutive (SAME SIDE) Interior Angles Converse:

If consecutive interior angles are __________________, then the lines are __________________.

Example:

Non Example:

Using the converses to determine if lines are parallel

3

6

l

k

2

6

j

k

92° l

k 88°

25° j

k

105°

130°

j

k

28° l

k

106°

137°

96° j

k 84°

H K

J I

3. Which pairs of angles need to be supplementary for AB || CD? (2 possible answers)

2. 1.

Example: Which lines, IF ANY, are parallel? Justify your reasoning with appropriate vocabulary.

1. 2. 3.

4. 5. 6.

7. 8. 9.

Example: Find the value of x that makes l // m. Justify your solution with appropriate vocabulary.

Example:

(A) Find the value of x that makes a // b.

(B) Find the value of y that makes a // c.

(C) Is b // c? Why or why not?

122°

l

k

58° m

105° 75°

A B

C D

55°

55°

E

F

G H

I

92° l

k 88°

l

k