Title: Angles
1Angles
2What 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
3Types 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.
5Angle Addition Postulate
- If point B is in the middle of then
6Vertical Angles
- Two angles whose sides form 2 pairs of opposite
rays vertical angles are congruent!!
7Adjacent Angles
- Two coplanar angles that have a common side and a
common vertex. - They have NO common interior points!
Adjacent
Nonadjacent
8Complementary Angles
- Two angles whose sum of their measures is 90
degrees.
Example 1
Example 2
9Supplementary Angles
- Two angles whose sum of their measures is 180
degrees.
Example 1
Example 2
10Linear Pair
- These are formed when two adjacent angles form a
line their measures add up to 180 degrees.
11Angle Bisector
- A ray that divides an angle into two congruent
angles.
bisects
12Perpendicular 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?.
13What 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!
14Sticky Note Time!!
- Draw the following
- is bisected by ray AM
15Angles and Algebra
X ________________
16Example 2
X __________________
17Example 3
X _________________
18Example 4
and are supplementary, 38,
4x 20. Draw and label the figure.
Also, find the value of x.
19Angle Relationships and Parallel Lines
20Transversal
- A line that intersects two coplanar lines at two
distinct points.
Transversal
21Corresponding Angles
22Alternate Interior Angles
23Same Side Interior Angles
24Alternate Exterior Angles
25Same Side Exterior Angles
26State the relationship between and .
Then, set up the equation for and .
Relationship __________ Equation ____________
Relationship __________ Equation ____________
27Example 1
x ________________
28Example 2
x ________________
29Example 3
x ________________
30Example 4
x ________________