Download Theorems about Parallel Lines

Line and Angle Relationships
Sec 6.1
GOALS:
To learn vocabulary
To identify angles and relationships
of angles formed by tow parallel lines
cut by a transversal
Vocabulary
Line
l
A
l or AB
B
Ray
A
Angle
B
A
sides
vertex
B
AB
C
ABC or B
Types of Angles

Acute angles – angles that have measures between 0 and

Right angles – angles that have measures equal to

Obtuse angles – angles that have measures between
90
90 and 180

Straight angles – angles that have measures equal to
180
90
Special Pairs of Angles

Vertical angles – opposite angles formed by intersecting lines.
Vertical angles are congruent.
3
1
4
1 and 2 are vertical angles
1  2
2
Special Pairs of Angles

Adjacent angles – angles that have the same vertex, share a
common side, and do not overlap.
A
B
1 2
C
1 and 2 are adjacent angles
mABC  m1  m2
Special Pairs of Angles

Complementary angles – angles whose sum is
90
ABD and DBC are commplementary angles
A
D
50
B
40
C
mABC  mABD  mDBC
mABC  50  40  90
Special Pairs of Angles

Supplementary angles – angles whose sum is
180
A and B are supplementary angles
140
A
B
40
mA  mB  180
Examples
Perpendicular Lines

Perpendicular lines – lines that intersect at right angles
h
k
k h
Parallel Lines

Parallel lines – two lines in a plane that never intersect or
cross
h
k h
k
Transversal
A line that intersects two or more other lines is called a
transversal. Eight angles are formed when a transversal
intersect two lines.
t
2
4
6
8
5
7
1
3
Corresponding Angles Postulate
Corresponding angles are those in the same position on the two
lines in relation to the transversal.
If two parallel lines are cut by a transversal, then corresponding
angles are congruent.
1  5
2
4
6
8
5
7
1
3
2  6
3  7
4  8
Alternate Interior Angles Theorem
Alternate interior angles are those on opposite sides of the
transversal and inside the other two lines.
If two parallel lines are cut by a transversal, then alternate interior
angles are congruent.
4  5
2
4
6
8
5
7
1
3
3  6
Alternate Exterior Angles Theorem
Alternate exterior angles are those on opposite sides of the
transversal and outside the other two lines.
If two parallel lines are cut by a transversal, then alternate exterior
angles are congruent.
1  8
2
4
6
8
5
7
1
3
2  7
Example
Given:
Find: x
k h
Alternate Exterior Angles Are Congruent
k
h
x
72
Example
k h
Given:
Find: x and the angle measure
Alternate Interior Angles Theorem
k
35
x
h
Example
2  5 m5  62
k h
Given:
Find the angles shown.
Alternate Interior Angles Theorem
m2  180  118  62
definition of supplementary angles
2
5
h
so m3  118
Con sec utive Interior Angles Theorem
118°
k
m2  m3  180 and m2  62,
3
4
4  3
Vertical angles are congruent
Students
k h
Given:
Find: All other angle measures
m3  m4  m7  30
k
30 1
2 3
h
4 5
6 7
m1  180  30  150  m2  m5  m6
Homework

Page 259
13-15, 19-22, 30-33, 47-49