Transcript Postulate 16: Corresponding Angles Converse If two lines are cut by

Geometry 3.3
Big Idea: Prove Lines
are Parallel
The converses of the
theorems we learned
yesterday are true which
leads to new theorems.
(Remember, not all converses
are true, but these are.)
Postulate 16: Corresponding
Angles Converse
If two lines are cut by a
transversal so that the
corresponding angles are
congruent, then the lines are
parallel.
Ðx @ Ðy
L1 || L2
Alternate Interior Angles Converse:
If two lines are cut by a transversal
so that the alternate interior angles
are congruent, then the lines are
parallel.
m || n
Alternate Exterior Angles Converse:
If two lines are cut by a transversal
so that the alternate exterior
angles are congruent, then the
lines are parallel.
a
b
Ð1@ Ð8
a || b
Consecutive Interior Angles
Converse:
If two lines are cut by a transversal
so that the consecutive interior
angles are supplementary, then the
lines are parallel.
Ð4 +Ð6 =180
m || n
Transitive Property of Parallel
Lines
If two lines are parallel to the same
line, then they are parallel to each
other.
p
q
r
If p || q and q || r, then p || r.
Example: Find the value of x that
m
(3x + 5)
makes m || n.
n
65
Example: Is m || n? m
75
n
105