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1.4 Angles Obj: State AAP and the definition of angle bisector and use them to find angle measures.


Angle • Formed by two rays or segments with the same endpoint E Side F

• Notation:

Side

G

Vertex


Naming an Angle: • 1. Use three points – Vertex must be the middle

• 2. Use vertex • 3. Use a number


Example 1 • Name each angle in every way possible. A C

1 B

2

D


Classifying Angles • Acute – measure between 0 and 90

• Right – measure of 90

• Obtuse – Measure between 90 and 180

• Straight – measure of 180 Angle


Adjacent Angles • Angles with a common vertex and a common side, but no common interior points • Adjacent


Angle Addition Postulate AAP •m∠AOB + m∠BOC = m∠AOC B C A

O


AND…. • m∠DOE + m∠EOF = 180 E

D

O

F


Congruent Angles • Two angles with equal measures • Notation


Angle Bisector • Ray or segment that divides an angle into two congruent adjacent angles

30° 30°


Example 2 • Segment AL bisects ∠KAT. Find x. • m∠1 = 7x +3 K • m∠2 = 6x + 7 L 2 3 1 T S A


Example 3 • m∠1 = x, m∠3 = 4x. Find x.

K L

S

3 A

2 1

T


Homework… • Pages 21-22 • 1-22, 26, 29-33 Odd • Written Exercises


Answers from Quiz Review: • • • • • • •

1. A 2. B 3. A 4. A 5. A 6. A 7. A

8. B 9. B 10. B 11. A 12. B


• • • • • • • •

13. AB=22, midpoint=-4 14. CD=25, midpoint=-24.5 15. Ray XW 16. PY=YQ 17. TP=16 and x=7 18. n=4 and CD=6 19. x=6, EF=29, FG=22 20. -6


Notes 1.4