Notes 1.4
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![Page 1: Notes 1.4](https://reader035.fdocuments.net/reader035/viewer/2022062305/568bd3411a28ab2034907c6f/html5/thumbnails/1.jpg)
Warm Up-9/17/09 #3
• Find the coordinate of the midpoint of AB if the coordinate of A is 7 and the coordinate of B is 201. Draw a diagram for credit!
![Page 2: Notes 1.4](https://reader035.fdocuments.net/reader035/viewer/2022062305/568bd3411a28ab2034907c6f/html5/thumbnails/2.jpg)
1.4 Angles
Obj: Use AAP and the definition of angle bisector to find angle measures.
![Page 3: Notes 1.4](https://reader035.fdocuments.net/reader035/viewer/2022062305/568bd3411a28ab2034907c6f/html5/thumbnails/3.jpg)
Angle
• Formed by two rays or segments with the same endpoint
• Notation: Side
Side
Vertex
F
G
E
![Page 4: Notes 1.4](https://reader035.fdocuments.net/reader035/viewer/2022062305/568bd3411a28ab2034907c6f/html5/thumbnails/4.jpg)
Naming an Angle:
• 1. Use three points– Vertex must be the middle
• 2. Use vertex
• 3. Use a numberSide
Side
Vertex
F
G
E
1
![Page 5: Notes 1.4](https://reader035.fdocuments.net/reader035/viewer/2022062305/568bd3411a28ab2034907c6f/html5/thumbnails/5.jpg)
Example 1
• Name each angle in every way possible.
21
B
A
C
D
![Page 6: Notes 1.4](https://reader035.fdocuments.net/reader035/viewer/2022062305/568bd3411a28ab2034907c6f/html5/thumbnails/6.jpg)
Classifying Angles• Acute
– measure between 0 and 90• Right
– measure of 90• Obtuse
– Measure between 90 and 180• Straight
– measure of 180Angle
![Page 7: Notes 1.4](https://reader035.fdocuments.net/reader035/viewer/2022062305/568bd3411a28ab2034907c6f/html5/thumbnails/7.jpg)
Adjacent Angles
• Angles with a common vertex and a common side, but no common interior points
• Adjacent
![Page 8: Notes 1.4](https://reader035.fdocuments.net/reader035/viewer/2022062305/568bd3411a28ab2034907c6f/html5/thumbnails/8.jpg)
Angle Addition PostulateAAP
•mAOB + mBOC = mAOCB
A
O
C
![Page 9: Notes 1.4](https://reader035.fdocuments.net/reader035/viewer/2022062305/568bd3411a28ab2034907c6f/html5/thumbnails/9.jpg)
AND….
• mDOE + mEOF = 180
D F
E
O
![Page 10: Notes 1.4](https://reader035.fdocuments.net/reader035/viewer/2022062305/568bd3411a28ab2034907c6f/html5/thumbnails/10.jpg)
Congruent Angles• Two angles with equal measures
• Notation: m1 = m2• Or: 1 2
• How to mark the diagram:• More than one pair of angles?
1
2
![Page 11: Notes 1.4](https://reader035.fdocuments.net/reader035/viewer/2022062305/568bd3411a28ab2034907c6f/html5/thumbnails/11.jpg)
Angle Bisector
• Ray or segment that divides an angle into two congruent adjacent angles
3030
![Page 12: Notes 1.4](https://reader035.fdocuments.net/reader035/viewer/2022062305/568bd3411a28ab2034907c6f/html5/thumbnails/12.jpg)
Example 2
• Segment AL bisects KAT. Find x. • m1 = 7x +3• m2 = 6x + 7
321
S T
K
L
A
![Page 13: Notes 1.4](https://reader035.fdocuments.net/reader035/viewer/2022062305/568bd3411a28ab2034907c6f/html5/thumbnails/13.jpg)
Example 3
• m1 = x, m3 = 4x. Find x.
321
S T
K
L
A
![Page 14: Notes 1.4](https://reader035.fdocuments.net/reader035/viewer/2022062305/568bd3411a28ab2034907c6f/html5/thumbnails/14.jpg)
Homework…
• Pages 21-22• 1-22, 26, 29, 31, 33 • Written Exercises