Download 5.2

5.2 Proving That
Lines Are Parallel
Objective:
After studying this section, you will be able to
apply the exterior angle inequality theorem
and use various methods to prove lines are
parallel.
An exterior angle of a triangle is formed
whenever a side of the triangle is extended to
form an angle supplementary to the adjacent
interior angle.
Adjacent Interior
angle
E
D Exterior angle
F
Remote Interior
angle
Theorem 30: The measure of an exterior angle of
a triangle is greater than the measure of either
remote interior angle.
Theorem 31: If two lines are cut by a transversal
such that two alternate interior
angles are congruent, the lines are
parallel.
(short form: Alt. int. s  ll lines.)
Given: 3  6
Prove: a ll b
a
3
b
6
Theorem 32: If two lines are cut by a transversal
such that two alternate exterior
angles are congruent, the lines are
parallel.
(short form: Alt. ext.s  ll lines.)
Given: 1  8
Prove: a ll b
a
1
b
8
Theorem 33: If two lines are cut by a transversal
such that two corresponding
angles are congruent, the lines are
parallel.
(short form: corr.s  ll lines.)
Given: 2  6
Prove: a ll b
a
2
b
6
Theorem 34: If two lines are cut by a transversal
such that two interior angles on the
same side of the transversal are
supplementary, the lines are parallel.
Given: 4 supplement ary to 6
Prove: a ll b
a
4
b
6
Theorem 35: If two lines are cut by a transversal
such that two exterior angles on the
same side of the transversal are
supplementary, the lines are parallel.
Given: 2 supplement ary to 8
Prove: a ll b
a
2
b
8
Theorem 36:If two coplanar lines are
perpendicular to a third line, they are
parallel.
a
b
Given: a  c and b  c
Prove: a ll b
c
Given: a  c and b  c
a
b
Prove: a ll b
1
2
c
Given: 1  2
MAT  THM
Prove: MATH is a parallelogram
A
1
M
T
3
4
2
H
Given: 2  3
1 is supplement ary 3
Prove: FROM is a TRAPEZOID
Note: A trapezoid is a four-sided figure
with exactly one pair of parallel sides.
S
R
F 2
3
O
1
M