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

Converse Angle Theorems Chp 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.

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

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.

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

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

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

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

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 – 105 + 75) Angle x and the other 75⁰ angle are corresponding and congruent. x