Download Geometry Chapter 3 – Parallel and Perpendicular Lines Spring 2009

Geometry
Chapter 3 – Parallel and Perpendicular Lines Spring 2009
Section 3-2
Proving Lines Parallel
Part I…..Converse of Section 3-1 Theorems and Postulates.
Converse of Corresponding Angles Postulate
Given two lines and a transversal.
Converse of Alternate Interior Angles Theorem
Given two lines and a transversal.
If the corresponding angles are ____________
Then the two lines are parallel.
If the alternate interior angles are ______________
Then the two lines are parallel.
Figure 1.
If _______
Figure 2.
_______,
If _______
then _____||_____
_______,
then _____||_____
Converse of Same-Side Interior Angles Theorem
Given two lines and a transversal.
Converse of Alternate Exterior Angles Theorem
Given two lines and a transversal.
If the same-side interior angles are ____________
Then the two lines are parallel.
If the alternate exterior angles are ______________
Then the two lines are parallel.
Figure 3.
If _______
_______ = 180,
Figure 4.
If _______
then _____||_____
then
_______,
_____||_____
Part II………Examples
1)
a) Given
b) Given
. Which lines (if any) are parallel?
. Which lines (if any) are parallel?
Geometry
Chapter 3 – Parallel and Perpendicular Lines Spring 2009
Which lines (if any) are parallel. Justify answer with a theorem or postulate.
2)
3)
Part III…..Algebra and angle pairs.
Find the value of x for which
1)
2)
3) Using the given information, determine which lines (if any) are
parallel, justify the conclusion.
a)
b)
c)