
Transversal: a line that intersects two
coplanar lines at two different points.
T (transversal)
n
5
1
m
6
3
4
2
7
8

The angles formed by a transversal have
special properties.
Alternate interior angles
T
n
∠1 and ∠2 are alt. int.
angles
∠3 and ∠4 are alt. int.
angles
1
m
3
4
2

Same-side interior angles
T
n
1
∠1 and ∠4 are sameside int.
∠3 and ∠2 are sameside int.
m
3
4
2

∠2 and ∠6 are
corresponding
Corresponding Angles
T
n
5
1
6
3
∠1 and ∠7 are
corresponding
m
∠4 and ∠5 are
corresponding
∠3 and ∠8 are
corresponding
4
2
7
8
T (transversal)
1. Name a pair of
alt. int. angles
1
2. Name a pair of
same-side int.
3. Name 2 pairs of
corresponding.
2
3 4
n
5
7
m
6
8

Corresponding Angles Postulate (3-1)
◦ If a transversal intersects two parallel lines, then
corresponding angles are congruent.
∠1 ≅ ∠2
Alternate Interior Angles Theorem (3-1)
◦ If a transversal intersects two parallel lines, then
alternate interior angles are congruent.
Same Side Interior Angles Theorem (3-2)
o If a transversal intersects two parallel lines, then
same-side interior angles are supplementary.
∠1 ≅ ∠3
m∠1 + m∠2 = 180
3
1
2
Given: a ‖ b  what you know (either from a picture or
statement)
Prove: ∠1 ≅ ∠2  what you must show
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.



Prove theorem 3-2 (If a transversal intersects two
parallel lines, then same-side interior angles are
supplementary.)
Given:
3 2
Prove: ∠1 and ∠2 are
1
supplementary


∠6 = 50°
Find the
measures of the
missing angles

Find the value of x and y
x°
50°
y°
70°

Find the values of x and y, then find the
measure of the angles.
2x°
y°
(y-50)°

Pg 119-120
1-7, 10, 11-16, 17, 23