Download Proving lines are PARALLEL

GEOMETRY
Section 3 - 2
Proving lines are PARALLEL
NOTES/PRACTICE
*So – if you knew you had parallel lines, you would be able to make conclusions about
corresponding angles, alternate interior angles, alternate exterior angles, same-side
interior angles and same-side exterior angles – but, would you be able to make those
conclusions without parallel lines?
CORRESPONDING ANGLES POSTULATE SAYS: _____________________________________
____________________________________________________________________________
__________________________________________________________________________.
What would the converse statement be?
CONVERSE OF THE CORRESPONDING ANGLES POSTULATE: _________________________
____________________________________________________________________________
_________________________________________________________________________.
Reason in Proof: ______________________________________________________________.
QUICK PROOF:
1
a
b
Given: 1  2
2
Statements
Prove: a  b
Reasons
GEOMETRY
Section 3 - 2
Proving lines are PARALLEL
NOTES/PRACTICE
Write the converse statement of the theorem, and then, complete the proof of the
converse theorem. YOU ARE PROVING THAT LINES ARE PARALLEL, YOU DO NOT GET TO
START WITH LINES ARE PARALLEL!!!
Alternate Interior Angles Theorem: If parallel lines are cut by a transversal, then alternate
interior angles are congruent.
Converse of the Alternate Interior Angles Theorem: ________________________________
___________________________________________________________________________.
PROVE that the lines are parallel first, and then you can use this theorem!!! Hint: You need to
show that corresponding angles are congruent.
Given: 1  3
Prove: m  n
m
n
Statements
1 3
2
Reasons
REASON IN PROOF: ________________________________________________________
Another one!!!
Same – Side Exterior Angles Theorem: If parallel lines are cut by a transversal, then same –
side exterior angles are supplementary.
Converse of the Same – Side Exterior Angles Theorem:______________________________
___________________________________________________________________________.
PROVE that lines are parallel first, and then you can use this theorem!!! Hint: You can either
show alternate interior angles congruent OR corresponding angles congruent.
GEOMETRY
Section 3 - 2
Proving lines are PARALLEL
NOTES/PRACTICE
4
Given: 4 and 2 are supplementary
Prove: m  n
Statements
1
m
n
3
2
Reasons
REASON IN PROOF: ___________________________________________________________
*THE OTHER TWO ARE VERY SIMILAR PROOFS, SO I WILL NOT MAKE YOU DO THOSE!! BUT
YOU DO HAVE TO WRITE THEM! 
Alternate Exterior Angles Theorem: If parallel lines are cut by a transversal, then alternate
exterior angles are congruent.
Converse of the Alternate Exterior Angles Theorem: ________________________________
___________________________________________________________________________.
REASON IN PROOF: ____________________________________________________________
Same – Side Interior Angles Theorem: If parallel lines are cut by a transversal, then same –
side interior angles are supplementary.
Converse of the Same - Side Interior Angles Theorem: ______________________________
___________________________________________________________________________.
REASON IN PROOF: ___________________________________________________________