Integrated 2 Chapter 8 – Parallel and Perpendicular Lines Spring 2009
Section 8-1 Notes Proving Lines Parallel
Part I…..Converse of Chapter 7 Theorems and Postulates.
A – Converse of Corresponding Angles Postulate:
Write the Converse of the ‘Parallel Lines Postulate’ from Chapter 7:
If two lines are intersected by a _________________ and _________________________________ then, _______________________.
Do you think this converse is true? Yes or No: __________
The converse can be assumed to be true, therefore it is a ________________________.
B – Converse of the Alternate Interior Angles Theorem:
Write the Converse of the Alternate Interior Angle Theorem (Parallel Lines Theorem 1) from chapter 7:
If two lines are ______________________________________________and _____________________________________________, then ________________________________________________________________________________________________________
Do you think the converse is true or false? ______________
In order for something to be a theorem, you have to be able to prove that it is true. Using the converse of the parallel lines postulate (in part A), prove that the converse of the Alternate Interior Angles theorem is true: t
Given: _______________________________ m
1
_______________________________
2 k
3
Prove: _____________________________
Is the converse a theorem? Yes or No: ____________
Converse of the Co-Interior Angles Theorem:
Write the Converse of the Co-Interior Angle Theorem (Parallel Lines Theorem 2) from chapter 7:
If two lines are ______________________________________________and _____________________________________________, then ________________________________________________________________________________________________________
Do you think the converse is true or false? ______________
In order for something to be a theorem, you have to be able to prove that it is true. Using the converse of the parallel lines postulate (in
Part A), prove that the converse of the Co-Interior Angles theorem is true (Draw a picture and label it to help you):
Given: _______________________________ t m
_______________________________
1
2 k
3
Prove: _____________________________
Is the converse a theorem? Yes or No: __________

Integrated 2 Chapter 8 – Parallel and Perpendicular Lines Spring 2009
Part II………Examples
1) a) Given – m∠1 = m∠2 . Which lines (if any) are parallel?
b) Given – m∠2 = m∠3 . Which lines (if any) are parallel?
Which lines (if any) are parallel. Justify answer with a theorem or postulate (write it out!).
2) 3)
Part III…..Algebra and angle pairs.
Find the value of x for which 𝑎 ∥ 𝑡
1) 2)
3) Using the given information, determine which lines (if any) are parallel, justify the conclusion using a theorem or postulate. a) ∠6 is supplementary to ∠7 b ) m∠9 = m∠6 c) m∠5 = m∠2