1. Warm Up
Find the value of x: 1. 2.

2. Converse Angle Theorems
Chp 3.3

3. Review of the Term “Converse”
Conditional statements have a hypothesis (p) and a conclusion (q):
If Mrs. York is in a bad mood (p), then she will eat a lot of chocolate (q).
CONVERSE means you just switch the p and the q:
If Mrs. York eats a lot of chocolate (q), then she is in a bad mood (p)
Some theorems in geometry (like the angle pair theorems we learned) have matching CONVERSE theorems.

4. Corresponding Angles Converse Theorem
Here is the theorem you already know (corresponding angles theorem): IF
THEN
two parallel lines are cut by a transversal
Corresponding angles are congruent
Here is the corresponding angles CONVERSE theorem:
Two lines are cut by a transversal and corresponding angles are congruent IF
THEN
The two lines must be parallel

5. Corresponding Angles Converse Theorem - Example
** in order for the lines to be parallel , the corresponding angles MUST be congruent. So:
3x + 5 = 65
Use the Corresponding Angle Converse Theorem to write an equation
3x = 60
Subtraction Property Equality
x = 20
Division Property Equality
** so if x = 20, the corresponding angles are congruent, and that means line m is parallel to line n.

6. Alternate Interior Angles Converse Theorem
Theorem you already know (alternate interior angles theorem):
two parallel lines are cut by a transversal
Alternate interior angles are congruent IF
THEN
Here is the alternate interior angles CONVERSE theorem:
Two lines are cut by a transversal and alternate interior angles are congruent IF
THEN
The two lines must be parallel

7. Alternate Exterior Angles Converse Theorem
Theorem you already know (alternate exterior angles theorem):
two parallel lines are cut by a transversal
Alternate exterior angles are congruent IF
THEN
Here is the alternate exterior angles CONVERSE theorem:
Two lines are cut by a transversal and alternate exterior angles are congruent IF
THEN
The two lines must be parallel

8. Consecutive Interior Angles Converse Theorem
Theorem you already know (consecutive interior angles theorem):
two parallel lines are cut by a transversal
Consecutive interior angles are supplementary IF
THEN
Here is the consecutive interior angles CONVERSE theorem:
The two lines must be parallel
Two lines are cut by a transversal and consecutive interior angles are supplementary IF
THEN

9. Transitive Property of Parallel Lines
If two lines are parallel to the same line, then they are parallel to each other

10. Examples: 5x + 8 = 53 Alternate Interior Angles Converse Thm 5x = 45
Subtraction Prop. Equality
x = 9
Division Prop. Equality
x + 73 = 180
Consecutive Interior Angles Converse Thm
x = 107
Subtraction Prop. Equality
They are parallel. Angle x is 75⁰ because it is a linear pair with 105⁰ (180 – ) Angle x and the other 75⁰ angle are corresponding and congruent. x