Download 5-2-proving-that-lines-are-parallel

Adv. Geometry
Chapter 5 Section 2 Notes
Name __________________________________
Proving that Lines are Parallel
B
Exterior Angle Inequality Theorem: The measure of an exterior angle of a
triangle is greater than the measure of either remote interior angle.
A
C
D
Example: Find the restrictions on x (what must it be less than and greater than).
3x  18
30
Parallel Line Theorems:
31. If alternate interior angles are congruent then the lines are parallel.
32. If alternate exterior angles are congruent then the lines are parallel.
33. If corresponding angles are congruent then the lines are parallel.
34. If interior angles on the same side of the transversal are supplementary then the lines are parallel.
35. If exterior angles on the same side of the transversal are supplementary then the lines are parallel.
36. If coplanar lines are perpendicular to a third line then the lines are parallel.
m
n
l
Examples: State which lines are parallel and write the theorem that justifies your answer. Highlight the
line that the angles share, then highlight in another color the other lines that form the angle.
1.
N
2.
P
Q
M
S
O
R
L
P
1
Adv. Geometry
Chapter 5 Section 2 Notes
Name __________________________________
3.
4.
D
A
S
Q
B
F
C
P
T
R
E
5. Find the value of x so that m||n.
10x
6. Find the value of x so that m||n.
m
m
6x  4
4x  6
14 x  8
n
n
Proof Example:
N
C
1. Given: CR  NP
OS  RP
CO  NS
Prove: CR
O
1
2
R
S
P
NP
Statements
Reasons
2