Download ANGLES

• Sequence (day 1)
– Use classroom ex
• Types of angles, naming, adj,
– Interior of angle
– Postulate
– Class exercises
Day 2
– Adj / bisector
– Class ex
– Assumptions (day 2)
Warm - up
•
Draw the following and create your own
intersection
– Line AB and line t intersecting
– Plane Q and line XY intersecting
– Plane K and plane M intersecting
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1.4
ANGLES
An angle is a geometric figure that consists of
two rays that share a common endpoint.
The common
endpoint of the
two rays is called
the vertex of the
angle
The two rays
are called the
sides of the
angle.
Naming an Angle
A
B
1
C
L ABC or L CBA
OR
L B or L 1
This confusing…
A
B
C
D
• Can we use just the vertex to name these
angles?
How many angles are there?
A
B
1
3
2
C
D
Name the vertex of  3
State another name for 3
State another name for 1
B
2 3 4
A
1
9 8
E
7 6
D
5
C
Angle Measurements
• We measure the size of an angle using
degrees.
• We measure the size of an angle using a
protractor
HOW DO WE USE A
PROTRACTOR?
Questions 7 - 12
Right Angle
A right angle is an angle measuring
exactly 90 degrees.
You use a protractor
to measure angles.
This angle
measures 90
degrees. It is
a right angle.
Acute Angle
An acute angle is an angle measuring
between 0 and 90 degrees.
This angle is less than
90 degrees. It is called
an acute angle.
“Ohhhh look at how a cute the little angle is…..”
Obtuse Angle
An obtuse angle is an angle measuring
between 90 and 180 degrees.
This angle is greater than
90 degrees. It is called an
obtuse angle.
Straight Angle
• A straight angle is 180 degrees.
A straight angle
Is a straight _____?
Congruent Angles
• Angles that have equal measure
Definition: Adjacent Angles
Two angles in a plane that have..
1. a common vertex
2. and a common side but no common
interior points.
Common Side
No Common interior
Points
Common Vertex
T – Adjacent
F – Not adjacent
2
1
T – Adjacent
F – Not adjacent
2
1
T – Adjacent
F – Not adjacent
1
2
T – Adjacent
F – Not adjacent
1
2
Bisector of a segment
• A line, segment, ray or plane that
intersects the segment at its midpoint.
3
3
A
B
P
Something that is
going to cut
directly through
the midpoint
Definition: Angle Bisector
• The ray that divides an angle into two
congruent adjacent angles
B
BX bisects L ABC
Name the two
congruent angles
C
X
A
Angle Addition Postulate
• If point B lies in the interior of  AOC,
– then m  AOB + m  BOC = m  AOC.
– What is the interior of an angle?
If  AOC is a straight angle
and B is any point not on AC, then m  AOB
+ m  BOC = 180.
Why does it add up to 180?
Assumptions
• There are certain things that you can
conclude from a diagram and others that
you can’t.
What can you Assume?
A
D
Be Careful
B
C
E
What you can Assume?
1.
2.
3.
4.
5.
All points shown are coplanar
A, B, C are collinear
B is between A and C
ABC is a straight angle
D is in the interior of ABE
A
D
B
6. ABD and DBE are adjacent angles.
C
E
What you can’t Assume?
• AB BC
• ABD  DBE
• CBE is a right angle
A
D
B
C
E
Arc marks –
indicate
congruent
angles
A
D
Tick marks –
indicate
congruent
segments
B
E
Indicates a 90
degree angle
C
Marks are used to
indicate conclusions
about size in a diagram.
Lessons Learned…
1. Don’t Assume !
2. Follow this rule: You can draw
conclusions about position, but not about
size.
3. Use markings to help you find out
information about the diagram
•
•
•
•
•
B
2 3 4
A
1
9 8
E
7 6
D
Name the right angle
State another name for 6
State another name for 2
State another name for 9
Name the angle adjacent to 4
that is not 3
5
C