Identifying Angles
Transversal: A line that intersects two coplanar lines at two distinct
points.
l
a
b
m
k
c
How many angles are formed by a transversal?
Identifying Angles
Alternate Interior Angles: Nonadjacent interior angles
that lie on opposite sides of the transversal.
Same-Side Interior Angles: Angles that lie on the same
side of the transversal between the two lines it intersects
Corresponding Angles: Angles that lie on the same side
of the transversal in corresponding positions relative to
the two lines it intersects
5 1
2
6
7 3
8 4
Same-Side Interior Angles
5 1
6 2
7 3
8 4
5
6
1
2
7 3
8 4
Identifying Angles
Alternate Exterior Angles: Nonadjacent exterior angles
that lie on opposite sides of the transversal.
Same-Side Exterior Angles: Angles that lie on the same
side of the transversal outside of the two lines it intersects
Alternate Exterior Angles
5
1
6 2
7 3
8
4
Same-Side Exterior Angles
5 1
6 2
7 3
8
4
Let’s Apply What We Have Learned, K?
Name the transversal and the two lines that form each angle pair.
Then name the angle pair.
1) 1 and 2
A
6
1
3
C 4
2
5
D
B
2) 5 and ACD
3) ABD and CDB
You Guys Try Some
Give a name for the angle pairs given.
1) 8 and 4
1
3
5
7
6
2
4
2) 4 and 5
3) 5 and 3
4) 3 and 2
8
5) 2 and 7
6) 7 and 1
You Guys Try Some
Give a name for the angle pairs given.
1) 8 and 4
1
3
5
7
6
8
2
4
2) 4 and 5
3) 5 and 3
4) 3 and 2
5) 2 and 7
6) 7 and 1
Properties of Parallel Lines
t
1
l
Note: Notation for
parallel lines
2
m
Postulate 3-1: Corresponding Angles Postulate:
If a transversal intersects two parallel lines, then
corresponding angles are congruent.
1  2
Properties of Parallel Lines
Let’s say this
angle is 72°…
Alternate Interior Angles are congruent!!!
Properties of Parallel Lines
t
a
b
3 2
1
Theorem 3-1: Alternate Interior Angles Theorem
If a transversal intersects two parallel lines, then alternate
interior angles are congruent.
1  3
Proof of Alternate Interior Angles Theorem
t
a
Given : a || b
4
3 2
1
b
Prove : 1  3
Statements
Reasons
a || b
2. 1  4
1.
3. 4  3
3.
4. 1  3
4.
1.
2.
Properties of Parallel Lines
Same-Side Interior Angles are supplementary!!!
Properties of Parallel Lines
t
a
b
3 2
1
Theorem 3-2: Same-Side Interior Angles Theorem
If a transversal intersects two parallel lines, then same-side
interior angles are supplementary.
m1 m2  180
Properties of Parallel Lines
Alternate Exterior Angles are congruent!!!
Properties of Parallel Lines
a
1 2
b
3
Theorem 3-3: Alternate Exterior Angles Theorem
If a transversal intersects two parallel lines, then alternate
exterior angles are congruent.
1  3
Proof of Alternate Exterior Angles Theorem
Given : a || b
Prove : 1  4
Statements
a
1
b
2
3 4
Reasons
a || b
2. 1  2
3. 2  4
1.
4. 1  4
4.
1.
2.
3.
Properties of Parallel Lines
Same-Side Exterior Angles are supplementary!!!
Properties of Parallel Lines
a
1 2
b
3
Theorem 3-4: Same-Side Exterior Angles Theorem
If a transversal intersects two parallel lines, then same-side
exterior angles are supplementary.
m2  m3  180
Sum It Up
If a transversal intersects two parallel lines…
Angle Pair
Corresp. Angles
Alt. Int. Angles
Alt. Ext. Angles
S-S Int. Angles
S-S Ext. Angles
Property
Properties of Parallel Lines
Use the given angle to find the missing angles. Justify
each answer.
68˚
1
2
Let’s Apply What We Have Learned, K?
Find the values of x and y in the diagram below.
52°
y°
66°
x°
Find the values of x and y in the diagram below.
Homework #11
Pg 131 #1-9, 11-16, 29