Download Geometry: Section 3.3 Proofs with Parallel Lines

Geometry: Section 3.3
Proofs with Parallel Lines
What you will learn:
1. Use the Corresponding Angles Converse
2. Construct parallel lines
3. Prove theorems about parallel lines
4. Use the Transitive Property of Parallel Lines
Theorem 3.5 Corresponding Angles Converse
If two lines are cut by a transversal so that
corresponding angles are congruent
____________________________________,
then
the lines are parallel
____________________________________
Note: We just switched the hypothesis and
conclusion of the Corresponding Angles
Theorem, hence the converse. The converses
of the Alternate Interior Angles Theorem, the
Alternate Exterior Angles Theorem and the
Consecutive Interior Angles Theorem are also
true.
3 x  5  2 x  4  180
5 x  1  180
8 x  12  6 x
2 x  12  0
8 x  5  80  180
8 x  85  180
5 x  181
x  36.2
2 x  12
x6
8 x  95
x  11.875
Example: Construct a line parallel to the line m through
point P using corresponding angles.
P
m
1) WZ bisects VWY, ZWY  X
1) Given
2) VWZ  ZWY
2) Def. of Bisects
3) VWZ  X
3) Substitution
) WZ || XY
) Corr. Angles
Converse
Theorem 3.9 Transitive Property of Parallel Lines
If two lines are both parallel to the same line,
the lines are parallel to each other
then _____________________________
If m || p and p || r,
then m || r
m
p
r
HW: pp 142 – 144 /
3 – 9, 13 – 16, 21, 22, 25, 30, 34, 36