Angle Relationships

Vocabulary

Transversal: a line that intersects two or more lines at different points.

Exterior Angles: <1, <2, <7, <8

12

78

34

56

Interior Angles:<3, <4, <5, <6

34

56

Same-Side Interior Angles:<3 and <5; <4 and <6

Same-Side Interior Angle

Theorem

If two parallel lines are cut by a transversal then each pair ofsame-side interior angles is supplementary

Converse of the Same-Side Interior

Angle TheoremIf two lines are cut by a transversal and the same-side interior angles are supplementary, then the lines are parallel.

132º48º

m

p

l

Since 132 + 48 = 180, m ║ p

1

8

2

7

Alternate exterior angles: 1 and 8 2 and 7

Alternate Exterior Angle TheoremIf two parallel lines are cut by

a transversal, then alternate exterior angles are congruent.Converse of the Alternate Exterior Angle TheoremIf two lines are cut by a transversal, and alternate exterior angles are congruent, then the lines are parallel.

75

75

p

q

g

Since alternate exterior angles are congruent, p ║ q

3

6

4

5

Alternate interior angles: 3 and 6 4 and 5

Alternate Interior Angle

TheoremIf two parallel lines are cut by a transversal then each pair of alternate interior angles is congruent.

Converse of then

Alternate Interior Angle

Theorem

If two lines are cut by a transversal, and alternate interior angles are congruent, then the lines are parallel.

Corresponding angles:

1 and 5 2 and 6

3 and 7 4 and 8 1

5

2

6

34

78

Corresponding Angle PostulateIf two parallel lines are cut by a

transversal then each pair of corresponding angles are congruent.

Converse of the Corresponding Angle Theorem

If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.

e

h

k

165º

165º

Since the corresponding angles are congruent, e ║ h.

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

Parallel Transversal Theorem

If two lines are parallel to the same line, then they are parallel to each other.

abc

a ║ b

mn

p

m ║ n

Perpendicular Transversal

TheoremIn a plane if a line is perpendicular to one of two parallel lines then it is alsoperpendicular to the other .

m

n

p

Since m n and m p, then n p.