Transcript 9/16 Angles and Their Measures notes File

Angles and Their Measures
Unit 1 Day 4

Do Now
 Match the angle with its classification
Acute
Right
Obtuse
Straight
Angles
 Angle: two different ________ sharing a(n)
___________________
 The rays are called the sides of the angle.
 The initial point is called the vertex of the angle.
Naming Angles
 We can name this angle _______, _______ or _______.
 Ex. 1 Name the angles in the second figure.
Measuring Angles
 The measure of angle A is denoted _____________.
 We can measure angles with a _______________ using units
called _______________.
 Angles that have the same measure are called
______________________.
 Angles are _____________
 Angle measures are ____________
C
A
B
Protractor Postulate
 The rays of an angle can be lined up with the real numbers from
0 to 180 (as though on a protractor).
 The measure of an angle is equal to the absolute value of the
difference between the real numbers corresponding to its two
rays.
C
A
B
D
Interior vs. Exterior
 A point is in the interior of an angle if
______________________________________
 A point is in the exterior of an angle if
_______________________________________
Angle Addition Postulate
 If D is in the interior of ABC, then
mABD + mDBC = _______
 Ex. 2 Given mRQS = 62 and mSQP = 18, find mRQP.
 Ex. 3 Given mPQS = 33 and mRQP = 58, find mSQR.
 In this class (for now), we will restrict angle measurements
to between 0 and 180.
 Acute:
 Right:
 Obtuse:
 Straight:
Classifying Angles
 Ex. 4 Classify the following angles
 LMN
 LMP
 NMQ
 LMQ
Adjacent Angles
 Two angles are adjacent angles if they share a
common vertex and side but have no common
interior points.
Ex. 4: Drawing Adjacent Angles
a) Draw two adjacent angles RSP and RST so that RST is
acute.
b) … RST is obtuse.
Closure
 JKL is a straight angle, and mJKM is 115º. H is a
point in the interior of JKM, and mHKL is 130º.
What is mHKM?