Download Angles and Transversals

3-1 Lines and Angles
Geometry
LINES AND ANGLES
Warm Up
2) The soccer team scored 3 goals in each of their first two games, 7 goals in the
next game, and 2 goals in each of the last four games. What was the average
(mean) number of goals the team scored per game?
Warm Up
Solve the equation:
= -20
= -0.8
= 9
= -1
=
MCC7.G.5. Use facts about
supplementary, complementary,
vertical, and adjacent angles in a multistep problem to write and solve simple
equations for an unknown angle in a
figure.
Formative
Essential Questions
How can I use the special angle
relationships – supplementary,
complementary, vertical, and adjacent – to
write and solve equations for multi-step
problems?
PARALLEL LINES
Lines that do not intersect
B
l
A
m
D
C
• Notation:
l || m
AB || CD
Examples of Parallel Lines
•
•
•
•
Opposite sides of windows, desks, etc.
Parking spaces in parking lots
Parallel Parking
Streets in a city block
PERPENDICULAR LINES
Lines that intersect to form a right angle
m
n
• Notation: m  n
• Key Fact: 4 right angles are formed.
Ex. of Perpendicular Lines
Acute Angle – any
angle less than 90º
Right Angle – a 90º angle
Obtuse Angle - any angle larger than 90º
Complementary Angles – angles that add up to 90º
Supplementary Angles – angles that add up to 180º
Adjacent Angles - angles that share a common vertex
and ray…angles that are back to back.
*Vertex – the “corner” of the angle
*Ray – a line that has an endpoint
on one end and goes on
forever in the other direction.
Congruent Angles – Angles with equal measurement
A ≅ B denotes that A is congruent to B.
Transversal - a line that intersects a set of
parallel lines
t
Vertical Angles
Two angles that are opposite angles at intersecting
lines. Vertical angles are congruent angles.
t
1 2
3 4
1   4
2   3
Vertical Angles
Find the measures of the missing angles
t
125 
? 
125
55
? 
55 
Linear Pair
Two adjacent angles that form a line. They
are supplementary. (angle sum = 180)
t
1+2=180
2+4=180
4+3=180
3+1=180
1 2
3 4
5
7
6
8
5+6=180
6+8=180
8+7=180
7+5=180
Supplementary Angles/
Linear Pair
Find the measures of the missing angles
t
108? 72 
108
? 
180 - 72
Corresponding Angles
Two angles that occupy corresponding positions when
parallel lines are intersected by a transversal…same
side of transversal AND same side of own parallel line.
Corresponding angles are congruent angles.
t
Top Left
Top Right
1
3
Bottom Left
Top Left
Bottom Left
2
4
Bottom Right
5
6 Top Right
7
8
Bottom Right
1   5
2   6
3   7
4   8
Corresponding Angles
Find the measure of the missing angle
t
145  35 
? 
145
Alternate Interior Angles
Two angles that lie between parallel lines on
opposite sides of the transversal. These angles
are congruent.
t
1
2
3
4
5 6
7
8
3   6
4   5
Alternate Interior Angles
Find the measure of the missing angle
t
82 
98  ?82 
Alternate Exterior Angles
Two angles that lie outside parallel lines
on opposite sides of the transversal. They
are congruent.
t
1
2
3
4
5 6
7
8
2   7
1   8
Alternate Exterior Angles
Find the measure of the missing angle
t
120 
60 
?
120 
Same Side Interior Angles
Two angles that lie between parallel lines
on the same sides of the transversal.
These angles are supplementary.
t
1
2
3
4
3 +5 = 180
4 +6 = 180
5 6
7
8
*Also known as Consecutive Interior Angles
Same Side Interior Angles
Find the measure of the missing angle
t
135 
?45 
180 - 135
Same Side Exterior Angles
Two angles that lie outside parallel lines
on the same side of the transversal.
These angles are supplementary.
t
1
2
3
4
1 +  7 = 180
2 +  8 = 180
5 6
7
8
*Also known as Consecutive Exterior Angles
Same Side Exterior Angles
Find the measure of the missing angle
t
135 
?
45 
180 - 135
1,5
3,7
2,6
3,6
5,4
1,8
2,7
3,5
4,6
1,7
2,8
4,8
equivalent
equivalent
equivalent
supplementary
supplementary
112º
112º
68º
68º
112º
68º
68º
112º
Closing
What is a transversal?
Name the types of equivalent angles.
Name the types of supplementary
angles.