Download Section 3.4 Day 1 Proving Lines Are Parallel

Week 2
Warm Up
10.24.11
State the converse of each:
1) If ∠1 is a right angle, then m ∠1 = 90⁰.
2) If m∠1 + m∠2 = 180⁰, then ∠1 and ∠2 are supplementary.
Re 1
( 4x + 7 )⁰
77⁰
( 4x + 7 )⁰ + 77⁰ = 180⁰
4x + 7 + 77 = 180
4x + 84 = 180
4x = 180 - 84
4x = 96
x = 24
Geometry
3.4 Day 1
I will prove that two lines are
Parallel.
P 16
Corresponding Angles Converse
If two lines are cut by a transversal so that
corresponding angles are congruent, then the lines
are parallel.
2
1
j
k
If ∠1 ≅ ∠2, then j ∥ k.
Theorem
3.8
Alternate Interior Angles Converse
If two lines are cut by a transversal so that the
alternate interior angles are congruent, then the
lines are parallel.
j
2
1
k
If ∠ 1 ≅ ∠ 2, then j ∥ k.
Ex 1
Prove:
j∥k
3 j
2
1
Step
∠1 ≅ ∠2
k
Reason
Given
∠2 ≅ ∠3
Vertical Angles Theorem
∠1 ≅ ∠3
Transitive Property of Equality
j∥k
P16
Theorem
3.9
Consecutive Interior Angles Converse
If two lines are cut by a transversal so that
consecutive interior angles are supplementary,
then the lines are parallel.
j
2
1
k
If m∠ 1 + m∠ 2 = 180⁰, then j ∥ k.
Theorem
3.10
Alternate Exterior Angles Converse
If two lines are cut by a transversal so that the
alternate exterior angles are congruent, then the
lines are parallel.
4
j
k
5
If ∠ 4 ≅ ∠ 5, then j ∥ k.
Ex 2
60⁰
4x⁰
m
n
m and n will be parallel
if 60⁰ + 4x⁰ are supplementary.
60⁰ + 4x⁰ = 180⁰
4x = 180 - 60
4x = 120
x = 30
m ∥ n if
x = 30
Ex 3
k
Is k parallel to j ?
yes
T3.8
j
Why?
Do: 1
Find the value of x that makes j and k parallel.
j
k
Assignment:
(4x + 21)⁰
(7x + 9)⁰
Textbook Page 153, 10 - 25 all and #28