Angles Intro , tranversals

1
Introduction to Angles and Triangles
Introduction to angles
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Math is a language

• Line extends indefinitely, no thickness
  
• or width
• Line segment part of a line, begin and
• end point
• Ray part of a line, starts at a point, goes
• indefinitely
• Angle - formed by two lines, segments
• or rays coming from a common point
• Vertex - common point at which two lines
• or rays are joined

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Degrees Measuring Angles
We measure the size of an angle using degrees.
Example Here are some examples of angles and
their degree measurements.
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Acute Angles An acute angle is an angle
measuring between 0 and 90 degrees. Example
                                                 
              
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Right Angles A right angle is an angle measuring
90 degrees. Example                       
                                         
90
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Complementary Angles Two angles are called
complementary angles if the sum of their degree
measurements equals 90 degrees. Example These
two angles are complementary.
                                                  
                             
Together they create a 90 angle
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Obtuse Angles An obtuse angle is an angle
measuring between 90 and 180 degrees. Example
                                                 
                
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Straight Angle A right angle is an angle
measuring 180 degrees. Examples
                                      
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Supplementary Angles Two angles are called
supplementary angles if the sum of their degree
measurements equals 180 degrees. Example
These two angles are supplementary.
                                                  
                    
These two angles sum is 180 and together the
form a straight line                            
                     
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Review
State whether the following are acute, right, or
obtuse.
3.
5.
acute
1.
right
obtuse
?
4.
2.
acute
?
obtuse
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Complementary and Supplementary
Find the missing angle.
1. Two angles are complementary. One measures
65 degrees. 2. Two angles are supplementary.
One measures 140 degrees.
Answer 25
Answer 40
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Complementary and Supplementary
Find the missing angle. You do not have a
protractor. Use the clues in the pictures.
2.
1.
x
x
55
165
X35
X15
13
1.
x
x
90
y
z
y
z
x
2.
x
110
y
y
z
z
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Vertical Angles are angles opposite each other
when two lines intersect                    
1.
90 and y are vertical angles
x and z are vertical angles
The vertical angles in this case are equal,
will this always be true?
110 and y are vertical angles
2.
x and z are vertical angles
Vertical angles are always equal
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Vertical Angles
Find the missing angle. Use the clues in the
pictures.
x
X58
58
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Parallel lines transversals and their angles
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Parallel Lines
What You'll Learn
You will learn to identify the relationships
among pairs of interior and exterior angles
formed by two parallel linesand a transversal.
In geometry, two lines in a plane that never
intersect , have the same slope, are called
____________.
parallel lines
parallel lines are always the same distance apart
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Parallel Lines and Transversals
In geometry, a line, line segment, or ray that
intersects two or more lines at different points
is called a __________
transversal
The lines cut by a transversal may or may not be
parallel.
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Parallel Lines and Transversals

• We will be most concerned with transversals that
  cut parallel lines.

2
1
3
4

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

5
6
8
7
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Parallel Lines and Transversals
Two lines divide the plane into three regions.
The region between the lines is referred to as
the interior.
The two regions not between the lines is referred
to as the exterior.
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Parallel Lines and Transversals
When a transversal intersects two lines, _____
angles are formed.
eight
These angles are given special names.
1. Interior angles , 3,4,5,6 lie between the two
parallel lines.
2. Exterior angles 1,2,7,8 lie outside the two
lines.
3. Alternate Interior angles 46, 53 opposite
sides of the transversal and lie between the
parallel lines
t
5. Consecutive Interior angles 45, 36 on the
same side of the transversal and are between the
parallel lines
4. Alternate Exterior angles 17, 28 Are on the
opposite sides of the transversal and lie outside
the two lines
6. Corresponding angles 15, 48, 26, 37 on
the same side of the transversal one is exterior
and the other is interior
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Name the pairs of the following angles formed by
a transversal.
Alternate Interior angles
Corresponding angles
Consecutive Interior angles
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Congruent Same shape and size The symbol
means that the shapes, lines or angles
are congruent
two shapes both have an area of 36 in2 , are they
congruent?
Numbers, or expressions can have equal
value.. In Geometry, we use congruent to
describe two or more objects, lines or angles as
being the same
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Parallel Lines and Transversals
Alternate interior angles are _________.
congruent
2
1
3
4
5
6
7
8
25
Parallel Lines and Transversals
Alternate exterior angles is _________.
congruent
?
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Parallel Lines and Transversals
consecutive interior angles is _____________.
supplementary
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Transversals and Corresponding Angles
corresponding angles is _________.
congruent
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Transversals and Corresponding Angles
Concept Summary
Concept Summary Congruent Supplementary
Types of angle pairs formed when a transversal
cuts two parallel lines.
consecutive interior
alternate interior
alternate exterior
corresponding
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Transversals and Corresponding Angles
s t and c d. Name all the angles that
arecongruent to ?1. Give a reason for each
answer.
corresponding angles
?3 ? ?1
vertical angles
?6 ? ?1
alternate exterior angles
?8 ? ?1
corresponding angles
?9 ? ?1
alternate exterior angles
?14 ? ?1
corresponding angles
?11 ? ?9 ? ?1
corresponding angles
?16 ? ?14 ? ?1
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Lets Practice

• mlt1120
• Find all the remaining angle measures.

60
120
120
60
120
60
120
60
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Another practice problem
40

• Find all the missing angle measures, and name the
  postulate or theorem that gives us permission to
  make our statements.

180-(4060) 80
60
7
6
4
8
5
60
80
40
120
80
100
60
1
2
9
11
3
12
10
120
60
80
100