Download 3.3 Parallel Lines and Angle Relationships A transversal is a line

Geometry 1A
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3.3 Parallel Lines and Angle Relationships
A transversal is a line that intersects two coplanar lines at two distinct points.
t
a
1 2
4 3
5 6
b
8 7
Alternate interior angles
Alternate interior angles are angles that lie on opposite sides of the transversal in the
interior.
Angle Pairs:
Same-side interior angles
Same-side interior angles are angles that lie on the same side of the transversal in the
interior.
Angle Pairs:
Corresponding angles
Corresponding angles are ones at the same location at each intersection.
Angle Pairs:
Example 1: Classify each pair of angles as alternate interior angles, same-side interior
angles, or corresponding angles.
1.
2.
1
3.
1
1
2
2
2
4.
1
5.
6.
1
1
2
2
2
Corresponding Angles Postulate
If a transversal intersects two parallel lines,
then corresponding angles are congruent.
Alternate Interior Angles Theorem
If a transversal intersects two parallel
lines, then alternate interior angles
are congruent.
Same-Side Interior Angles Theorem
If a transversal intersects two parallel lines,
then same-side interior angles are supplementary.
Example 2: Find the measure of ∠1 and ∠2 . Justify each answer.
a.
b.
c.
2
o
100
1
o
1
135
o
75
1
2
2
Example 3: Find x and the measure of each angle.
a.
b.
x
c.
o
(7x)
(x – 26)
o
(x + 55)
(3x – 5)
o
o
o
Example 4: In the figure to the right, m || n. Find x.
a. m∠2 = ( 9 x − 2 ) , m∠4 = (10 x − 8 )


1
5
2
m
6
7
3
4
b. m∠6 = ( 4 x + 20 ) , m∠7 = ( 2 x + 4 )

8

Converse of the Corresponding Angles Postulate
If two lines and a transversal form corresponding angles that are congruent, then the
lines are parallel.
Converse of the Alternate Interior Angles Theorem
If two lines and a transversal form alternate interior angles that are congruent, then the
two lines are parallel.
Converse of the Same-Side Interior Angles Theorem
If two lines and a transversal form same-side interior angles that are supplementary,
then the two lines are parallel.
n
Example 4: Using the given information, which lines, if any, can you conclude are
parallel? Justify each conclusion with a theorem or postulate.
a. ∠ 3 is supplementary to ∠ 10
1 2
r
5 6
7 8
4 3
b. ∠3 ≅ ∠1
s
9 10
11 12
13 14
16 15
t
v
c. ∠6 ≅ ∠14
d. ∠7 ≅ ∠2
e. ∠11 ≅ ∠14
f. ∠4 ≅ ∠10