Download MCC8.G.5 Angles and Parallel Lines

MCC8.G.5
Angles and
Parallel Lines
Intersecting Lines
• Lines that cross at exactly one point.
• Think of an intersection, where two roads
cross each other.
Perpendicular Lines
• Lines that intersect to form right angles.
PARALLEL LINES
• Definition: lines that do not intersect.
• Think: railroad tracks!
• Here’s how it looks:
B
A
l
m
• This is how you write it:
D
C
l || m
AB || CD
• This is how you say it:
“Line l is parallel to line m” and “Line AB is parallel to line CD”
Examples of Parallel Lines
•
•
•
•
•
Hardwood Floor
Opposite sides of windows, desks, etc.
Parking slots in parking lot
Parallel Parking
Streets
Examples of Parallel Lines
• Streets: Belmont & School
Transversal
• Definition: A line that intersects two or more lines in a
plane at different points is called a transversal.
• Line t is a transversal here, because it intersects line m
and line n.
m
n
t
Vertical Angles & Linear Pair
Vertical Angles: Two angles that are opposite angles. Vertical
angles are congruent, which means they’re equal.
 1   4,  2   3,  5   8,  6   7
(The symbol  means congruent, in case you’ve forgotten)
Linear Pair:Supplementary angles that form a line (sum = 180)
These are linear pairs:
1 & 2 , 2 & 4 ,
4 &3, 3 & 1,
5 & 6, 6 & 8,
8 & 7, 7 & 5
1
3 4
5
7
6
8
2
Linear Pairs
• Two (supplementary and adjacent) angles
that form a line (sum=180)
1+2=180
2+4=180
4+3=180
3+1=180
t
1 2
3 4
5
7
6
8
5+6=180
6+8=180
8+7=180
7+5=180
Can you…
Find the measures of the missing angles?
t
108? 72 
108
? 
180 - 72
Complementary Angles
• Two angles whose measures add to 90˚.
Adjacent Angles
• Angles in the same plane that have a
common vertex and a common side.
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
Continued…..
Consecutive exterior angles
Corresponding Angles
Corresponding Angles: Two angles that occupy
corresponding positions.
 2   6,  1   5,  3   7,  4   8
1
3
5 6
7 8
2
4
Consecutive Angles
Consecutive Interior Angles: Two angles that lie between
parallel lines on the same sides of the transversal.
(Think “interior” as in, inside the parallel lines…)
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 2
m1 +m7 = 180º, m2 +m8 = 180º
3 4
5 6
7 8
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.
1 2
3 4
 2   7,  1   8
5 6
7
8
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.
Hint:
First, find angle 2!
Use the measure of
angle 1 to get your
started.
A
1
4
C
5
8
s
m<2=80° m<3=100° m<4=80°
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°
2
9
12
3
6
13 14
16 15
7
t
10
11
B
D
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
4
C
5
8
2. 35
s
3. 33
1
A
2
9
12
3
6
13 14
16 15
7
t
10
11
B
D