Unit 6 Congruence

1
Unit 6 Congruence

• Transversals

2
Warm Up
3
Definition

• Two lines are parallel if they lie in the same
  plane and do not intersect.
• If lines m and n are parallel we write

p
q
p and q are not parallel
m
n
4
Transversals

• A transversal for lines m and n is a line t that
  intersects lines m and n at two distinct points.
  We say that t cuts m and n.
• A transversal may also be a line segment and it
  may cut other line segments.

E
m
A
B
n
D
C
t
5

• When a transversal cuts parallel lines, special
  pairs of angles are formed that are sometimes
  congruent and sometimes supplementary.

6
Corresponding Angles
1
2
m
3
4
5
6
n
8
7
7
Vertical Angles
1
2
m
3
4
5
6
n
8
7
8
Alternate Interior Angles
m
3
4
6
5
n
9
Alternate Exterior Angles
1
2
m
n
7
8
10
Interior Angles on the Same Sideof the
Transversal
m
3
4
5
6
n
11
Exterior Angles on the Same Sideof the
Transversal

• When a transversal cuts two lines, exterior
  angles on the same side of the transversal are
  angles outside of the two lines on the same side
  of the transversal.

1
3
m
n
2
4
12
Labeling types of angles
Which angles are vertical? Which angles are
corresponding? Which angles are alternate
interior angles? Which angles are alternate
exterior?
b
a
c
d
f
e
g
h
13

• Practice Label the angles and tell how you know

A
B
D
C
40
E
F
G
H
Ex If ltC is 40, then ltD is 140 because they
must 180
14

• Practice Label the angles and tell how you know

A
B
D
C
E
F
G
H
112
15

• Practice Label each angle and tell how you know

A
B
38
D
C
E
F
G
H
16

• Practice Label each angle and tell how you know

x
2x 60