Download ANGLES

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
•Every angle is named by three letters. The middle letter
is the name of the vertex.
•Another way to name an angle is by the angle’s vertex.
•Look at the top of p.17 for other ways we can name
angles
L ABC or L CBA
OR
LB
A
Angle (ABC)
B
C
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
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?
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 the a cute little angle that 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 _____?
GAME TIME!
• The object of the game is to be
the first to raise your hand
and correctly name what type
of angle you see.
• The correct answer will be on the
following slide!!
• Good luck!
Acute
Angle
Obtuse
Angle
Right
Angle
Straight
Angle
GREAT
JOB!!
Protractor Postulate (pg.18)
• Read it on your own
• It basically tells us that we can use our
protractor to line up and measure the
degrees of angles (just as we lined up the
ruler to measure length)
• It also discusses absolute value, just like
with the number line
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?
Congruent Angles
• Angles that have equal measure
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
Common Roof
Duplex
No Common
Things
Common Wall
Duplex
Adjacent Angles
Common Roof
Common Vertex
Common Wall
Common Side
No Common things
inside my house
No Common Interior
Points
Remote time
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
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
Bisector of an Angle
• The ray that divides the angle into two
congruent adjacent angles (pg 19)
B
BX bisects L ABC
Name the two
congruent angles
C
X
A
Assumptions
• There are certain things that you can
conclude from a diagram and others that
you can’t.
Group Problem
A
D
B
C
E
What can you Assume?
A
D
Be Careful
B
C
E
What you can Assume?
1.
2.
3.
4.
5.
6.
All points shown are coplanar
AB, BD, and BE intersect at B.
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
7. 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
Practice on the White Boards
B
2 3 4
A
1
9 8
E
7 6
D
5
C
Name the vertex of  3
B
2 3 4
A
1
9 8
E
7 6
D
5
C
Name the right angle
B
2 3 4
A
1
9 8
E
7 6
D
5
C
State another name for 1
B
2 3 4
A
1
9 8
E
7 6
D
5
C
State another name for 6
B
2 3 4
A
1
9 8
E
7 6
D
5
C
State another name for 3
B
2 3 4
A
1
9 8
E
7 6
D
5
C
State another name for 4
B
2 3 4
A
1
9 8
E
7 6
D
5
C
State another name for 7
B
2 3 4
A
1
9 8
E
7 6
D
5
C
State another name for 2
B
2 3 4
A
1
9 8
E
7 6
D
5
C
State another name for 5
B
2 3 4
A
1
9 8
E
7 6
D
5
C
State another name for 9
B
2 3 4
A
1
9 8
E
7 6
D
5
C