1. Lesson 3 – 5 Proving Lines Parallel
Geometry
Lesson 3 – 5
Proving Lines Parallel
Objective:
Recognize angle pairs that occur with parallel lines.
Prove that two lines are parallel using angle relationships.

2. Review Angle Relationships
Alternate Interior
Alternate exterior
Consecutive Interior
Corresponding

3. Postulates Converse of Corresponding Angles Parallel Postulate
If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
Parallel Postulate
If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.

4. Theorems 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 two lines are parallel.
Consecutive interior angles converse
If two lines in a plane are cut by a transversal so that a pair of consecutive angles is supplementary, then the two lines are parallel.

5. Theorems Alternate Interior angles Converse
If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the two lines are parallel.
Perpendicular Transversal Converse
In a plane, if two lines are perpendicular to the same line, then they are parallel.

6. l II n l II m Alt. Int. Alternate Exterior angles
Given the following information, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer.
l II n
Alternate Exterior angles
l II m
Alt. Int.

7. l II m Corr. a II b Alt. Int. a II b Alt. Ext. l II m Cons. Int.
Given the following information, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer.
l II m Corr.
a II b Alt. Int.
a II b Alt. Ext.
Not possible.
Not possible
l II m Cons. Int.

8. 5x + 7 = 7x – 21 because Alt. Int. 7 = 2x – 21 28 = 2x 14 = x
Find the measure of angle MRQ so that LM and NP are parallel. Show work.
5x + 7 = 7x – because Alt. Int.
7 = 2x – 21
28 = 2x
14 = x
5(14) + 7
= 77

9. Homework
Pg – 7 all, 8 – 22 E, 34, 44 – 56 E