The two rays are called the sides of the angle.
The common endpoint of the two rays is called the vertex of the angle
An angle is a geometric figure that consists of two rays that share a common endpoint.
B
A
C
L ABC or L CBA OR L B
Angle (ABC)
•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
Naming an Angle
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?
This angle measures 90 degrees. It is a right angle.
You use a protractor to measure angles.
Right AngleA right angle is an angle measuringexactly 90 degrees.
This angle is less than 90 degrees. It is called an acute angle.
Acute AngleAn acute angle is an angle measuring between 0 and 90 degrees.
“Ohhhh look at the a cute little angle that is…..”
Obtuse Angle
This angle is greater than 90 degrees. It is called an obtuse angle.
An obtuse angle is an angle measuringbetween 90 and 180 degrees.
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!
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?
Adjacent Angles
Two angles in a plane that have..
1. a common vertex
2. and a common side but no common interior points.
Common Vertex
Common Side
No Common interior Points
Duplex Adjacent Angles
Common Roof Common Vertex
Common Wall Common Side
No Common things inside my house
No Common Interior Points
Bisector of a segment
• A line, segment, ray or plane that intersects the segment at its midpoint.
A
B
P
3
3
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)
Name the two congruent angles
B
AX
C
BX bisects L ABC
Assumptions
• There are certain things that you can conclude from a diagram and others that you can’t.
What you can Assume?
1. All points shown are coplanar
2. AB, BD, and BE intersect at B.
3. A, B, C are collinear
4. B is between A and C
5. ABC is a straight angle
6. D is in the interior of ABE
7. ABD and DBE are adjacent angles.
A
E
D
C
B
A
E
D
C
B
Marks are used to indicate conclusions about size in a diagram.
Tick marks – indicate
congruent segments
Arc marks – indicate
congruent angles
Indicates a 90 degree angle
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