12-2 Notes and answers Reg Geo.notebook -...
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122 Notes and answers Reg Geo.notebook 1 December 04, 2015 Nov 2510:09 PM Apply properties of arcs. Apply properties of chords. Objectives Nov 2510:09 PM A central angle is an angle whose vertex is the center of a circle. An arc is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them.
Transcript of 12-2 Notes and answers Reg Geo.notebook -...
122 Notes and answers Reg Geo.notebook
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Apply properties of arcs.
Apply properties of chords.
Objectives
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A central angle is an angle whose vertex is the center of a circle. An arc is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them.
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Minor arcs may be named by two points. Major arcs and semicircles must be named by three points.
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Example 1: Data Application
The circle graph shows the types of grass planted in the yards of one neighborhood. Find mKLF.
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Check It Out! Example 1
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Example 2: Using the Arc Addition Postulate
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Check It Out! Example 2a Find each measure.
mJKL
m∠KPL = 180° – (40 + 25)°
= 25° + 115°
mKL = 115°mJKL = mJK + mKL
= 140°
Arc Add. Post.
Substitute.
Simplify.
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Check It Out! Example 2b Find each measure.
mLJN
= 295°mLJN = 360° – (40 + 25)°
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Example 3A: Applying Congruent Angles, Arcs, and Chords
TV ≅ WS. Find mWS.
= 88 Simplify.
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Example 3B: Applying Congruent Angles, Arcs, and Chords
8C ≅ 8J, and m∠GCD ≅ m∠NJM. Find NM.
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Check It Out! Example 3a
PT bisects ∠RPS. Find RT.
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Check It Out! Example 3b
8A ≅ 8B, and CD ≅ EF. Find mCD. Find each measure.
25y° = (30y – 20)°20 = 5y4 = yCD = 25(4)mCD = 100°
mCD = mEF
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Find NP.
Example 4: Using Radii and Chords
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QR = 2(17.3) = PS ^ QR , so PS bisects QR.
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Assignment(p. 797) 9, 10, 12, 26(p. 806) 518, 2532, 38, 39
