Download Notes 1-4 - Robinson Schools

SB Geom 1­4 Completed.notebook
September 13, 2012
Lesson 1.4 Measure and Classify Angles
angle ­ consists of two different rays with the same endpoint
sides of the angle ­ rays with common endpoints
D
vertex ­ the endpoint
B
To name an angle:
­ use the vertex if only two rays
­ use three points with vertex in the middle
A
C
Example 1. Name three angles.
Aug 24­8:26 AM
Postulate 3. Protractor Postulate
Consider OB and a point A on one side of OB. The rays of the form OA can be matched one to one with the real numbers from 0 to 180.
Measure of <AOB is the absolute value of the difference between the real numbers for OA and OB.
Classifying Angles
Acute ­ an angle with a measure greater than zero and less than 90
Right ­ an angle with a ninety degree angle
Obtuse ­ an angle with a measure greater than 90 and less than 180
Straight ­ an angle with a measure with 180 degrees
Aug 24­8:33 AM
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SB Geom 1­4 Completed.notebook
September 13, 2012
How to measure angles with a protractor.
123oo
123
36o
Aug 24­8:38 AM
Example 2. Find the angle measure.
a. <KHJ
b. <GHK
c. <GHJ
d. <GHL
Guided Practice.
1. Name all the angles in the diagram at the right. Which angle is a right angle?
2. Draw a pair of opposite rays. What type of angle do the rays form?
Aug 24­8:43 AM
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SB Geom 1­4 Completed.notebook
September 13, 2012
Postulate 4. Angle Addition Postulate
If P is the interior of <RST, then the measure of <RST is equal to the sum of the measures of <RSP and <PST.
R
m<RST = m<RSP + m<PST
S
P
T
Example 3. m<LKN = 145 o, find m<LKM and m<MKN.
Aug 24­8:46 AM
Aug 24­8:56 AM
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SB Geom 1­4 Completed.notebook
September 13, 2012
congruent angles ­ two angles with the same measure
m<A = m<B
<A ≅ <B
Aug 24­8:58 AM
5. Identify all pairs of congruent angles in the diagram. 6. In the diagram, m<PQR = 130 o, m<QRS = 84 o, and m<TSR = 121 o. Find the other angle measures in the diagram.
angle bisector ­ a ray that divides an angle into two congruent angles
A
B
D
BD bisects <ABC so <ABD ≅ <DBC
C
Aug 24­9:01 AM
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SB Geom 1­4 Completed.notebook
September 13, 2012
Example 5. In the diagram at the right, VW bisects <XYZ, and m<XYW = 18 o. Find m<XYZ.
7. AC bisects <ABD. Find m<BAC and m<CAD.
4x ­ 10
2x +30
Aug 24­9:06 AM
Homework
Lesson 1-4
2-60 Evens
Aug 24­9:09 AM
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