1. Proving Lines Parallel
What You'll Learn
You will learn to identify conditions that produce parallel lines.
Reminder: In Chapter 1, we discussed “if-then” statements (pg. 24).
Within those statements, we identified the “__________” and the
“_________”.
hypothesis
conclusion
I said then that in mathematics, we only use the term
“if and only if”
if the converse of the statement is true.

2. Proving Lines Parallel
Postulate 4 – 1 (pg. 156):
IF ___________________________________,
THEN ________________________________________.
two parallel lines are cut by a transversal
two parallel lines are cut by a transversal
each pair of corresponding angles is congruent
each pair of corresponding angles is congruent
The postulates used in §4 - 4 are the converse of postulates that you already
know.
COOL, HUH?

3. Proving Lines Parallel
Postulate 4-2
In a plane, if two lines are cut by a transversal so that a pair
of corresponding angles is congruent, then the lines are
_______.
parallel 1 2 a b
If <1 ≅ <2,
then _____
a || b

4. Proving Lines Parallel
Theorem 4-5
In a plane, if two lines are cut by a transversal so that a pair
of alternate interior angles is congruent, then the two lines are _______.
parallel 1 2 a b
If <1 ≅ <2,
then _____
a || b

5. Proving Lines Parallel
Theorem 4-6
In a plane, if two lines are cut by a transversal so that a pair
of alternate exterior angles is congruent, then the two lines are _______.
parallel 1 2 a b
If <1 ≅ <2,
then _____
a || b

6. Proving Lines Parallel
Theorem 4-7
In a plane, if two lines are cut by a transversal so that a pair
of consecutive interior angles is supplementary, then the two lines are _______.
parallel 1 2 a b
If <1 + <2 = 180,
then _____
a || b

7. Proving Lines Parallel
Theorem 4-8
In a plane, if two lines are cut by a transversal so that a pair
of consecutive interior angles is supplementary, then the two lines are _______.
parallel
If a t and b t,
then _____ a b t
a || b

8. Proving Lines Parallel
We now have five ways to prove that two lines are parallel.
Concept
Summary
Show that a pair of corresponding angles is congruent.
Show that a pair of alternate interior angles is congruent.
Show that a pair of alternate exterior angles is congruent.
Show that a pair of consecutive interior angles is supplementary.
Show that two lines in a plane are perpendicular to a third line.

9. Proving Lines Parallel
Identify any parallel segments. Explain your reasoning. G A Y D R
90°

10. Proving Lines Parallel
Find the value for x so BE || TS. E B S T
(6x - 26)°
(2x + 10)°
(5x + 2)°

11. End of Lesson