Download 2.7 Angle Pair Relationships

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
3.2 Use Parallel Lines and Transversals
Objectives:
1. To find angle pair measurements with
parallel lines cut by a transversal
2. To prove theorems involving parallel lines
cut by a transversal
Transversal
A line is a transversal
if and only if it
intersects two or
more coplanar lines.
– When a transversal
cuts two coplanar
lines, it creates 8
angles, pairs of
which have special
names
Transversal
• <1 and <5 are
corresponding angles
• <3 and <6 are alternate
interior angles
• <1 and <8 are alternate
exterior angles
• <3 and <5 are
consecutive interior
angles
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
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.
Parallel Line Theorems
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.
Example 1
On the map below, 1st and 2nd Ave. are
parallel.
Example 1
A city planner proposes to locate a small
park on the triangular island formed by the
intersections of the four streets below.
Example 1
What are the measures of the three angles
of the garden? Answer in your notebook
Example 2: SAT
In the figure, if l || m,
what is the value of
x?
HINT: Find y 1st since there are
2 parts with y.
y=25
x=10
l
3y
2y+25
x+15
m
Example 3: SAT
In the figure, if l1 || l2
and l3 || l4, what is y
in terms of x.
THINK about it before
you look at the answer and
TRY!
y=180-x
2
l2
l3
l1
x
l4
y
y
Example 4
Prove the Alternate Interior Angle Theorem.
Given: l m
Prove: 3  6
TRY IT!!!
Example 5
Given: l m and m2  64
Prove: m7  64
You can EASILY do
THIS one!
Example 7
Find the values of x and y if k || l || m.
k
Did you try it??!?!
7x+9
l
x=13.8
y=11.2
7y-4
11x-1
m
2y+5