3.3 notes

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This document discusses six theorems for proving that two lines are parallel: (1) the corresponding angles converse theorem, (2) the alternate interior angles converse theorem, (3) the alternate exterior angles converse theorem, (4) the consecutive interior angles converse theorem, (5) using a paragraph proof, and (6) the transitive property of parallel lines theorem. It also assigns homework problems from page 165 involving using these theorems to prove lines are parallel.

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3.3 Prove Lines are Parallel September 26, 2011

3.3 Prove Lines are Parallel
Postulate 16: Corresponding Angles Converse
                        If 2 lines are cut by a transversal so the corresponding
                        angles are congruent, then the lines are parallel.

2 j
j // k
6 k

Example 1

Find the value of x that makes m // n.
(3x + 5) m

65 n

                           Guided Practice #1 with vertical partner

HW pg. 165 #414 evens, 2931, 34 & 35 1

3.3 Prove Lines are Parallel September 26, 2011

Theorem 3.4: Alternate Interior Angles Converse
                        If 2 lines are cut by a transversal so the alternate interior
                        angles are congruent, then the lines are parallel.
j // k j

5 4
k

Theorem 3.5: Alternate Exterior Angles Converse
                        If 2 lines are cut by a transversal so the alternate exterior
                        angles are congruent, then the lines are parallel.
j // k
1 j

k
8

Theorem 3.6: Consecutive Interior Angles Converse
                 If 2 lines are cut by a transversal so the consecutive
                 interior angles are supplementary, then the lines are parallel.
j // k
j
3
<3+<5=180
5 k

HW pg. 165 #414 evens, 2931, 34 & 35 2

3.3 Prove Lines are Parallel September 26, 2011

HW pg. 165 #414 evens, 2931, 34 & 35 3

3.3 Prove Lines are Parallel September 26, 2011

HW pg. 165 #414 evens, 2931, 34 & 35 4

3.3 Prove Lines are Parallel September 26, 2011

Paragraph Proof: written in paragraph form and in sentences
explaining the logical flow of argument

HW pg. 165 #414 evens, 2931, 34 & 35 5

3.3 Prove Lines are Parallel September 26, 2011

Theorem 3.7: Transitive Property of Parallel Lines
If 2 lines are parallel to the same line,
then they are parallel to each other.

HW pg. 165 #414 evens, 2931, 34 & 35 6

3.3 Prove Lines are Parallel September 26, 2011

HW pg. 165
#414 evens
2931,
34 & 35

HW pg. 165 #414 evens, 2931, 34 & 35 7

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