Download Geometry 3-5 Proving Lines Parallel

Geometry 3-5 Proving Lines Parallel
We've seen that, if we have parallel lines cut by a
transversal, we get special relationships among the angles
created. This time, we'll go the other way - we'll start from
angle relationships and prove that the lines are parallel.
Postulate 3.4 - Corresponding Angles Postulate
Converse: If two lines are cut by a transversal so that
corresponding angles are congruent, then the lines are
parallel.
Theorem 3.6 - Consecutive Interior Angles Converse: If
two coplanar lines are cut by a transversal so that a pair of
consecutive interior angles is supplementary, then the two
lines are parallel.
Theorem 3.7 - Alternate Interior Angles Converse: If two
coplanar lines are cut by a transversal so that a pair of
alternate interior angles is congruent, then the two lines are
parallel.
Find m JRS so that g || h.
JRS = 5x + 7; RSK = 7x - 21
5x + 7 = 7x - 21
28 = 2x
14 = x
m JRS = 5(14) + 7 = 77
J
P
g
QRS = 12x - 15; RSK = 8x - 5
12x - 15 + 8x - 5 = 180 20x - 20 = 180
QRS = 12(10) - 15 = 105
JRS = 180 - 105 = 75
L
S
R
Q
h
K
20x = 200
x = 10
Mf
Postulate 3.5 - Parallel Postulate: If given a line and a
point not on that line, then there is exactly one line through
the point parallel to the given line.
Theorem 3.5 - Alternate Exterior Angles Converse: If two
coplanar lines are cut by a transversal so that a pair of
alternate exterior angles is congruent, then the two lines are
parallel.
Theorem 3.8 - Perpendicular Transversal Converse: In a
plane, if two lines are perpendicular to the same line, then
they are parallel.
Based on the given information, determine which lines (if
any) are parallel. State the theorem and/or postulate that
1
justifies your answer.
2
~ 5
m || p, Alt Int Conv
2=
3
4
3~
1
m
||
n,
Corr
Conv
=
4 supp 5
n || p, Cons Int Conv
6
5
q
m
n
p