Download Geometry Section 3.4 Proving Lines Parallel

Geometry Section 3.4
Proving Lines Parallel
With the postulates and theorems of Section
3.3, we are given that lines are parallel and
make conclusions about the special angle
pairs. In this section, the process is reversed
as we look at the converses of the postulates
and theorems from Section 3.3.
Postulate 16: CAP Converse
If two lines are cut by a transversal and
corresponding angles are __________,
congruent
then
the lines are parallel.
Theorem 3.8: AIAT Converse
If two lines are cut by a transversal and
alternate interior angles are __________,
congruent
then
the lines are parallel.
Theorem 3.9: SSIAT Converse
If two lines are cut by a transversal and
same-side interior angles are ____________,
supplementary
then
the lines are parallel.
Theorem 3.10: AEAT Converse
If two lines are cut by a transversal and
alternate exterior angles are __________,
congruent
then
the lines are parallel.
Examples: Determine which lines, if any, will be parallel based
on the given information. If lines are parallel, give a reason
why (i.e. one of the converses).
a) 3  28
a // c
AEATConverse
b) 1  25
a // c
CAPConverse
c) m12  m15  180
d // e
SSIATConverse
Examples: Determine which lines, if any, will be parallel based
on the given information. If lines are parallel, give a reason
why (i.e. one of the converses).
d) m9  m16  180
None
e) 20  26
None
f) 8  13
a // b
AIATConverse
Example: Find the value of x that would make lines a and b parallel.
a. m3  3x  5, m6  2 x  4
3 x  5  2 x  4  180
5 x  1  180
5 x  181
a
4
1
2 3
5 6 b
87
x  36.2
c
b. m4  8 x  12, m8  6 x
8 x  12  6 x
 12  2 x
c. m1  8 x  5, m6  80
x6
8 x  5  80  180
8 x  85  180
8 x  95
x  11.875