3.2 Use Parallel Lines and Transversals
Objectives:
1. To make and prove
conjectures about
the angles formed
by a pair of parallel
lines and a
transversal
Assignment:
• P. 78: 15-20
• P. 87: 1-12
• Challenge Problems
Warm-Up
1. Using the lines on a
piece of paper as a
guide, draw a pair of
parallel lines. Now
draw a transversal
that intersects the
parallel lines. Label
the angles with
numbers.
Warm-Up
2. Place a patty paper
over the set of angles
<1, <2, <3, and <4 and
copy the two
intersecting lines onto
the patty paper.
3. Slide the patty paper
down and compare
angles 1 through 4 with
angles 5 through 8.
1 2
3 4
Warm-Up
2. Place a patty paper
over the set of angles
<1, <2, <3, and <4 and
copy the two
intersecting lines onto
the patty paper.
3. Slide the patty paper
down and compare
angles 1 through 4 with
angles 5 through 8.
1 2
3 4
Warm-Up
Do you notice a
relationship
between pairs of
corresponding,
alternate interior,
and alternate
exterior angles?
1 2
3 4
Transversal
A line is a
transversal if and
only if it intersects
two or more
coplanar lines.
1
3
5
7
When a transversal cuts
two coplanar lines, it
creates 8 angles, pairs of
which have special names
6
8
2
4
Transversal
Corresponding Angles
1
∠1 and ∠5
3
5
Alternate Interior Angles
∠3 and ∠6
7
6
8
2
4
Transversal
Alternate Exterior Angles
1
∠1 and ∠8
3
5
Same-Side Interior Angles
∠3 and ∠5
7
6
8
2
4
Exercise 1
Classify the pair of numbered angles.
Exercise 2
List all possible answers.
1. ∠2 and ___ are
corresponding ∠s
2. ∠4 and ___ are
same-side interior ∠s
3. ∠4 and ___ are
alternate interior ∠s
Four Window Foldable
Start by folding a
blank piece of paper
in half lengthwise,
and then folding it in
half in the opposite
direction. Now fold
it in half one more
time in the same
direction.
Four Window Foldable
Now unfold the paper,
and then while
holding the paper
vertically, fold down
the top one-fourth to
meet the middle.
Do the same with
the bottom onefourth.
Four Window Foldable
To finish your foldable,
cut the two vertical
fold lines to create
four windows.
Outside: Name
Inside Flap: Illustration
Inside: Postulate or
Theorem
Four Window Foldable
Corresponding Angles
Postulate
If two parallel lines are cut by
a transversal, then pairs of
corresponding angles are
congruent.
Alternate Interior Angles
Theorem
If two parallel lines are cut by
a transversal, then pairs of
alternate interior angles
are congruent.
Four Window Foldable
Alternate Exterior Angle
Theorem
If two parallel lines are cut by
a transversal, then pairs of
alternate exterior angles
are congruent.
Consecutive Interior Angles
Theorem
If two parallel lines are cut by
a transversal, then pairs of
consecutive interior angles
are supplementary.
Exercise 3
Prove the Alternate Interior Angle Theorem.
Given: l m
Prove: 3  6
Exercise 4
Given: l m and m2  64
Prove: m7  64
Exercise 5: SAT
In the figure, if l || m,
what is the value of
x?
l
3y
2y+25
x+15
m
Exercise 6: SAT
In the figure, if l1 || l2
and l3 || l4, what is y
in terms of x.
l2
l3
l1
x
l4
y
y
Exercise 7
Calculate each lettered angle measure.
Exercise 8
Find the values of x and y if k || l || m.
k
7x+9
l
7y-4
11x-1
m
2y+5
3.2 Use Parallel Lines and Transversals
Objectives:
1. To make and prove
conjectures about
the angles formed
by a pair of parallel
lines and a
transversal
Assignment:
• P. 78: 15-20
• P. 87: 1-12
• Challenge Problems