Transcript Lesson 2-4 - Teachers.Henrico Webserver

Lesson 2-4
Angles and
Parallel Lines
Lesson 2-4: Angles and Parallel
Lines
1
Transversal

Definition: A line that intersects two or more lines in a
plane at different points is called a transversal.

When a transversal t intersects line n and m, eight angles
of the following types are formed:
m
Exterior angles
Interior angles
Consecutive interior angles
Alternative exterior angles
Alternative interior angles
Corresponding angles
t
n
Lesson 2-4: Angles and Parallel
Lines
2
Vertical Angles & Linear Pair
Vertical Angles: Two angles that are opposite angles. Vertical
angles are congruent.
 1   4,  2   3,  5   8,  6   7
Linear Pair: Supplementary angles that form a line (sum = 180)
1 & 2 , 2 & 4 , 4 &3, 3 & 1,
5 & 6, 6 & 8, 8 & 7, 7 & 5
1
2
3 4
5
7
6
8
Lesson 2-4: Angles and Parallel
Lines
3
Angles and Parallel Lines

1.
2.
3.

1.
2.
If two parallel lines are cut by a transversal, then the
following pairs of angles are congruent.
Corresponding angles
Alternate interior angles
Alternate exterior angles
If two parallel lines are cut by a transversal, then the
following pairs of angles are supplementary.
Consecutive interior angles
Consecutive exterior angles
Continued…..
Lesson 2-4: Angles and Parallel
Lines
4
Corresponding Angles & Consecutive Angles
Corresponding Angles: Two angles that occupy
corresponding positions.
 2   6,  1   5,  3   7,  4   8
1
3
2
4
5 6
7 8
Lesson 2-4: Angles and Parallel
Lines
5
Consecutive Angles
Consecutive Interior Angles: Two angles that lie between parallel
lines on the same sides of the transversal.
m3 +m5 = 180º, m4 +m6 = 180º
Consecutive Exterior Angles: Two angles that lie outside parallel
lines on the same sides of the transversal.
1
m1 +m7 = 180º, m2 +m8 = 180º
3
4
5
7
Lesson 2-4: Angles and Parallel
Lines
2
6
8
6
Alternate Angles

Alternate Interior Angles: Two angles that lie between parallel
lines on opposite sides of the transversal (but not a linear pair).
 3   6,  4   5

Alternate Exterior Angles: Two angles that lie outside parallel
lines on opposite sides of the transversal.  2   7,  1   8
1
3
4
5
7
2
6
8
Lesson 2-4: Angles and Parallel
Lines
7
Example: If line AB is parallel to line CD and s is parallel to t, find
the measure of all the angles when m< 1 = 100°. Justify your answers.
A
1
4
C
5
8
m<2=80° m<3=100° m<4=80°
2
12
3
6
B
10
11
D
13 14
16 15
7
s
9
t
m<5=100° m<6=80° m<7=100° m<8=80°
m<9=100° m<10=80° m<11=100° m<12=80°
m<13=100° m<14=80° m<15=100° m<16=80°
Lesson 2-4: Angles and Parallel
Lines
8
Example: If line AB is parallel to line CD and s is parallel to t, find:
1. the value of x, if m<3 = 4x + 6 and the m<11 = 126.
2. the value of x, if m<1 = 100 and m<8 = 2x + 10.
3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20.
ANSWERS:
1. 30
1
A
4
C
5
8
2. 35
2
12
3
6
3. 33
Lesson 2-4: Angles and Parallel
Lines
B
10
11
D
13 14
16 15
7
s
9
t
9