Transcript 1.4 Measuring Angles - Cardinal O'Hara High School

1.4 Measuring Angles 9/13/12
• An angle is formed by two rays with the same
endpoint.
• The rays are the sides of the angle.
• The endpoint is the vertex of the angle.
• One way to measure the size of an angle is in degrees.
– To indicate the measure of an angle, write a lowercase m
in front of the angle symbol.
Naming an Angle
• You can name angles by:
– The vertex
– A point on each ray and the vertex
– A number
• When naming angles using three points, the vertex
must go in the middle.
A
BAC
CAB
1
• The interior of an angle is the region
containing all of the points between the two
sides of the angle.
• The exterior of an angle is the region
containing all of the points outside of an angle.
Naming Angles
• What are two other names for 1?
JMK
KMJ
Postulate 1.7 Protractor Postulate
• The Protractor Postulate allows you to find the
measure of an angle.
• The measure of the angle is the absolute value of
the difference of the real numbers paired with the
sides of the angle.
Protractor Postulate
• The Protractor Postulate and the calculation of
an angle measure are very similar to the Ruler
Postulate and the calculation of a segment
length.
Types of Angles
• You can classify angles according to their
measures.
This symbol indicates a
right angle.
Measuring and Classifying Angles
What are the measures of LKN , JKL, and JKN ?
•
Classify each angle as acute, right, obtuse, or straight.
Measuring and Classifying Angles
mLKN |145  0 | 145
OBTUSE
mJKL | 90 145|| 55| 55
ACUTE
mJKN | 90  0 | 90
RIGHT
Congruent Angles
• Angles with the same measure are congruent
angels.
IfmA  mB, thenA  B
Angle Addition Postulate
• If point B is in the interior of
AOC, then
mAOB  mBOC  mAOC.
Using the Angle Addition Postulate
• If the measure of angle RQT is 155, what are the
measures of angle RQS and angle TQS?
mRQS  mTQS  mRQT
(4 x  20)  (3x  14)  155
7 x  6  155
7 x  161
x  23
mRQS  4 x  20  4(23)  20  92  20  72
mTQS  3x  14  3(23)  14  69  14  83
More Practice!!!!!
• Classwork – Textbook p. 31 – 32 # 7 – 23 odd.
• Homework – Textbook p. 31 – 32 # 6 – 22
even.