Angles

1
Angles
2
What is an angle?

• Angle
• Formed by two rays with the same endpoint. The
  rays are the sides of the angle and the common
  endpoint is the vertex of the angle.

Named A, BAC, or CAB
3
Types of Angles

• Acute
• An angle whose measure is between 0 and 90
  degrees.
• Obtuse
• An angle whose measure is between 90 and 180
  degrees

4

• Right
• An angle whose measure IS 90 degrees.
• Straight
• An angle whose measure is 180 degrees.

5
Angle Addition Postulate

• If point B is in the middle of then

6
Vertical Angles

• Two angles whose sides form 2 pairs of opposite
  rays vertical angles are congruent!!

7
Adjacent Angles

• Two coplanar angles that have a common side and a
  common vertex.
• They have NO common interior points!

Adjacent
Nonadjacent
8
Complementary Angles

• Two angles whose sum of their measures is 90
  degrees.

Example 1
Example 2
9
Supplementary Angles

• Two angles whose sum of their measures is 180
  degrees.

Example 1
Example 2
10
Linear Pair

• These are formed when two adjacent angles form a
  line their measures add up to 180 degrees.

11
Angle Bisector

• A ray that divides an angle into two congruent
  angles.

bisects
12
Perpendicular Lines

• Always form 4 right angles.
• If we know that one angle of the intersecting
  lines is 90?, then the other 3 are also 90?.

13
What can we assume by looking at a figure?

• Can Assume
• Angles are adjacent
• Angles are vertical
• Angles form a linear pair

• Cannot Assume
• Angles are right
• Angles are complementary
• Angles are supplementary
• Must have additional information to prove these!

14
Sticky Note Time!!

• Draw the following
• is bisected by ray AM

15
Angles and Algebra

• Ex 1

X ________________
16
Example 2
X __________________
17
Example 3
X _________________
18
Example 4
and are supplementary, 38,
4x 20. Draw and label the figure.
Also, find the value of x.
19
Angle Relationships and Parallel Lines
20
Transversal

• A line that intersects two coplanar lines at two
  distinct points.

Transversal
21
Corresponding Angles

• They are congruent

22
Alternate Interior Angles

• They are congruent.

23
Same Side Interior Angles

• They are supplementary

24
Alternate Exterior Angles

• These are congruent.

25
Same Side Exterior Angles

• These are supplementary

26
State the relationship between and .
Then, set up the equation for and .
Relationship __________ Equation ____________
Relationship __________ Equation ____________
27
Example 1
x ________________
28
Example 2
x ________________
29
Example 3
x ________________
30
Example 4
x ________________