2. Properties of Parallel Lines What does it mean for two lines to be parallel? THEY NEVER INTERSECT! l m

3. Parallel Lines cut by a Transversal p l m 12 34 56 78 1) Transversal 2) Identify the Alternate Interior Angles.3) Identify the Corresponding Angles.4) Identify the Same Side Interior Angles. ALTERNATE INTERIOR ANGLES ARE CONGRUENTCORRESPONDING ANGLES ARE CONGRUENT S ame S ide interior angles are S upplementary 5) Identify the Alternate Exterior Angles. Alternate Exterior Angles are Congruent

4. Review Theorems: 1)Vertical angles are congruent. 2)Linear pairs are supplementary (180°) 3)The sum of the measures of the angles in a triangle is 180° Review Theorems: 1)Vertical angles are congruent. 2)Linear pairs are supplementary (180°) 3)The sum of the measures of the angles in a triangle is 180°

5. Find m<1 and m<2 and state the theorem(s) that justify your answer. 1) 2) 95° 1 2 80° 1 2

6. In the accompanying diagrams, find all the variables. 3) 4) x 37° 74° 5y4y

7. In the accompanying diagrams, find all the variables. 5) 6) (2x+10) (3x-20) (4x+9) 73°

8. Using the given information, determine if any lines are parallel, and if so, state which lines and theorem used. z m x y 12 34 5678 9101112 1413 7)<7 is supplementary to <6 8) <9 = <11 9) <5 = <9 10) <6 = <12

9. Proofs Involving Parallel Lines Part 1: Given Parallel Lines When you know that you are working with parallel lines you can use the theorems we learned yesterdays as reasons within your proof: A.Alternate interior angles are congruent, when lines are parallel. B.Corresponding angles are congruent, when lines are parallel. C.Alternate exterior angles are congruent, when lines are parallel. D.Same side interior angles are supplementary, when lines are parallel

10. Examples: StatementsReasons 1), and 1) Given 2) <1 = <A, <2 = <B 2)Alternate Interior angles, when lines //. 3) <A = <B3) Substitution Postulate

11. Part 2: Proving Lines Parallel To prove two lines parallel we can use the converse of many of our theorems involving parallel lines. A. If a pair of alternate interior angles are congruent, then the lines are parallel. B. If a pair of corresponding angles are congruent, then the lines are parallel. C. If a pair of same side interior angles are supplementary, then the lines are parallel. There are two more methods of proving lines are parallel. D. Two lines parallel to the same line are parallel to each other. (Transitive Property) l m p If and then

12. If and, then E. If two lines are perpendicular to the same line, then they are parallel.

13. 1) bisects, and 1) Given 2) <ABD = <CBD 2) A bisector divides the < into 2 congruent <‘s 3) <CBD = <CDB 3) If two sides of a Δ are congruent, then <‘s opposite are congruent 4) <ABD = <CDB 4) Substitution (or Transitive) 5) 5) If a pair of alternate interior angles are congruent, then the lines are parallel.

14. 1) Quad ABCD, and 1) Given 2) <BCA = <DAC 2)Alternate Interior angles, when lines //. 3) AC = AC3) Reflexive Postulate 4) ΔABC = ΔCDA4) SAS 5) <BAC = <DCA5) CPCTC 6) 6) If a pair of alternate interior angles are congruent, then the lines are parallel.