Download Geo 1.3 Measuring and Constructing Angles Student Notes

Geometry
Name:______________________
Date: ___________
Chapter 1: Foundations for Geometry
Section 1.3: Measuring and Construction Angles
Are you ready?
1) Draw AB and AC, where A, B, and C are noncollinear.
2) Draw opposite rays DE and DF.
Solve each equation.
3) 2x + 3 + x – 4 + 3x – 5 = 180
4) 5x + 2 = 8x – 10
Objectives of Lesson: ________________________________________
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Who uses this? Surveyors use angles to help them measure and map the
earth’s surface
An angle___________________________________________________
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Vertex: (in your own words)____________________________________
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The set ___________________________________________________
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Example 1: Naming Angles
A surveyor recorded the angles formed by a transit (point A) and three
distant points, B, C, and D. Name three of the angles.
Example 2
Write the different ways you can name the angles in the diagram.
The measure: ______________________________________________
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Degree (in your own words) ____________________________________
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Protractor Postulate
Using a Protractor
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Types of Angles
Example 3: Measuring and Classifying Angles
Find the measure of each angle. Then classify each as acute, right, or
obtuse.
YXZ:
ZXV:
YXW:
ZXW:
WXV:
Example 4
Use the diagram to find the measure of each angle. Then classify each as
acute, right, or obtuse.
1) AOD
4) BOA
2) EOC
5) DOB
3) COD
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Congruent Angles: __________________________________________
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Practice Constructing Congruent Angles
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Postulate 1-3-2 (Angle Addition Postulate)
Example 5: Using the Angle Addition Postulate
mDEG = 115°, and mDEF = 48°. Find mFEG
Example 6
mXWZ = 121° and mXWY = 59°. Find mYWZ.
Example 6a
mABD = 37° and m<ABC = 84°. Find mDBC.
Example 6b
mXWZ = 121° and mXWY = 59°. Find mYWZ.
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An Angle Bisector__________________________________________
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Practice Constructing Angle Bisectors
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Example 7: Finding the Measure of an Angle
KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find
mJKM.
Example 8: Find the measure of each angle.
QS bisects PQR, mPQS = (5y – 1)°, and mPQR = (8y + 12)°. Find mPQS.
Example 9: JK bisects LJM, mLJK = (-10x + 3)°, and mKJM = (–x + 21)°.
Find mLJM.
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Example 10:
A surveyor at point S discovers that the angle between peaks A and B is 3
times as large as the angle between peaks B and C. The surveyor knows that
∠ASC is a right angle. Find m∠ASB and m∠BSC.
Questions I have for next class:
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