1. 1-4: Measuring Angles

2. Parts of an Angle
Formed by the union of two rays with the same endpoint.
Called sides of the angle
Called the vertex of the angle
3 ways to name
BAC or CAB
A (Vertex) 1
Exterior A B
Interior 1 C

3. Types of Angles Congruent Angles Angles with the same measure Acute
Right
Obtuse
Straight
Congruent Angles
Angles with the same measure

4. Example 1: 1). Name the angle below.
Name the sides and the vertex of the angle. X Y Z 1
2). Label the 3 points on the figure below so that the angle has sides KQ and KN. Q K N

5. Protractor Postulate
Consider and a point on one side of Every ray of the form can be paired one to one with a real number 0 to 180. A B O

6. 135°
45° A D a d
Example 2: What is ?

7. Postulate 1-8: Angle Addition Postulate
If point B is in the interior of , then:
Example 3: If , what are and ?

8. Classwork: p. 31 #’s 6, 7, 12-14, 18, 20, 22, 23, 29-31

9. 1-5: Exploring Angle Pairs

10. Types of Angle Pairs Adjacent Angles Vertical Angles
Complementary Angles
Supplementary Angles
Two coplanar angles with a: _______________, ________________, _______________________________
common side
common vertex
no common interior points
Two angles whose sides are __________ ______
opposite
rays
Two angles whose measures have a sum of _______
Two angles whose measures have a sum of _______

11. Example 1: Use the diagram below. Is each statement true? Explain.
and are adjacent angles.
and are vertical angles.
and are supplementary.
Yes,
they have a common side
No,
they don’t share two pairs of opposite rays
Yes,
the sum of the angles is 180°

12. Assumptions About Angles
Assumptions you can make:
Angles are adjacent
Angles are adjacent and supplementary
Angles are vertical angles
Assumptions you can’t make:
Angles or segments are congruent
An angle is a right angle
Angles are complementary

13. Postulate 1-9: Linear Pair Postulate
A Linear Pair of angles are angles that are both supplementary and adjacent.
Ex 2 What are the measures of and ?

14. Theorem 2-1: Vertical Angle Theorem
Vertical angles are congruent
and
Example 3: What is the value of x? What are the angle measures?

15. Angle Bisector
A ________ which divides an angle into ______ _______________ angles.
ray
two
congruent
is an angle bisector.
Example 4: bisects If , what is ?

16. Homework: p. 38 # 7-23 odd, 26-32 even