3.5 Proving Lines Parallel Then: You used slope to identify parallel and perpendicular lines. Now: 1. Recognize angle pairs that occur with parallel line. 2. Prove that two lines are parallel. Review Converse: exchange the hypothesis and conclusion of a conditional statement. What is the converse of the following? If it is raining, then Josh needs an umbrella.
Postulate 3.4 Converse of Corresponding Angles If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. If 2 6, then j k.
Theorem 3.5 Alternate Exterior Angles Converse If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, then the lines are parallel. If 1 8, then j k.
Theorem 3.6 Consecutive Interior Angles Converse If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel. If m3 +m5 = 180, then j k.
Theorem 3.7 Alternate Interior Angles Converse If two lines in a plane are cut by a transversal so that a pair alternate interior angles is congruent, then the lines parallel. If 4 5, then j k.
Theorem 3.8 Perpendicular Transversal Converse In a plane, if two lines are perpendicular to the same line, then they are parallel. If k t, and l t, then k l. http://chieftainconverse.weebly.com/uploads/9/6/1/0/9610550/987963_orig.gif
Example 1: Given the following information, determine which lines, if any, are parallel. State the postulate or theorem to justify your answer. a. 3 7 b. 9 11 c. 2 16 d. m 5 + m 12 = 180
Example 2: Find the value of x that makes l m. Identify the postulate or theorem you used. a.
Example 2: Find the value of x that makes l m. Identify the postulate or theorem you used. b.
Example 2 cont. Find the value of x that makes l m. Identify the postulate or theorem you used. c.
Example 3: Proof 1 Given: 1 5, 15 5 Prove: l m, r s Statements Reasons 1. 15 5 1. _______________________ 2. 13 15 2. _______________________ 3. 5 13 3. _______________________ 4. r s 4. _______________________ 5. 1 5 5. _______________________ 6. l m 6. _______________________
Example 3: Proof 2 Given: 1 and 2 are complementary BC CD Prove: BA CD Statements Reasons 1. BC CD 1. __________________________ 2. mABC = m 1 + m 2 2. __________________________ 3. 1 and 2 are complementary 3. __________________________ 4. m 1 + m 2 = 90 4. __________________________ 5. mABC = 90 5. __________________________ 6. BA BC 6. __________________________ 7. BA CD 7. __________________________
3.5 Assignment #8-22 evens, 26,28, 33-35, 44-50 evens p. 211-214 #8-22 evens, 26,28, 33-35, 44-50 evens Proofs #26 & 28- on handout