Warm Up State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If mA + mB = 90°, then A and B are complementary. 3. If AB + BC = AC, then A, B, and C are collinear. If a + c = b + c, then a = b. If A and  B are complementary, then mA + mB =90°. If A, B, and C are collinear, then AB + BC = AC.

Correcting Assignment #21 (1-4, 7-10, 12-17)

Correcting Assignment #21 (18-20, 22)

3.3 - Proving Lines are Parallel Learning Target: I can prove lines are parallel

A converse of a theorem is found by exchanging the hypothesis and conclusion. The converse of a theorem is not automatically true. If it is true, it must be stated as a postulate or proved as a separate theorem.

In Section 3. 2, we got the Corresponding Angles Theorem and in 3 In Section 3.2, we got the Corresponding Angles Theorem and in 3.3 we get it’s converse. Notice the difference in the hypothesis and conclusions.

Yesterday, we also discussed theorems regarding Alternate Interior and Alternate Exterior Angles. We also found that Same Side Interior and Same Side Exterior Angles are supplementary, though our text does not call them out as separate theorems.

The converses of each of those theorems and postulates are also true and can be used to prove that two lines are parallel given a specific relationship between angle pairs

Reasons in Proofs and HW Exercises If the given information (hypothesis) is about parallel lines and you make a conclusion about an angle pair, then your reason will be one of the angle pair postulates or theorems from section 3.2. If the given information (hypothesis) is an angle pair relationship and you make the conclusion that the lines are parallel, then your reason will be one of the “converse of” postulates or theorems from section 3.3

a is parallel to b by the Converse of Interior Same Side Angles Postulate l is parallel to m by the Corresponding Angles Theorem and the Converse of Interior Same Side Angles Postulate a is parallel to b by the Converse of Alternate Exterior Angles Theorem

Assignment #22 - Pages 160-162 Foundation – (1-3, 6-10, 13-16) Core – (18-28 even, 31, 33, 39) Challenge - (42,44)