Bell Ringer Write an example of each of the following:

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Presentation transcript:

Bell Ringer 4-8-19 Write an example of each of the following: 1. Radius 2. Secant 3. Tangent 4. Chord 5. Diameter 6. Minor arc 7. Major arc 8. Central angle 9. Inscribed angle 10. Center

Arc Length Monday, April 8, 2019

Quick Definition Review Chord: a segment whose endpoints lie on a circle A B AB

Quick Definition Review Arc: an unbroken part of a circle

Quick Definition Review Minor Arc: an arc that is less than half of a circle. to name, use 2 points

Quick Definition Review Major Arc: an arc that is more than half of a circle. to name, use 3 points

Quick Definition Review Central Angle: an angle whose vertex is at the center of a circle

Quick Definition Review Inscribed Angle: an angle whose vertex is on a circle and whose sides are chords of the circle

Quick Definition Review Tangent: a line, ray, or segment that intersects the circle in only one point (perpendicular)

Quick Definition Review Secant: a line, ray, or segment that contains a chord

Arc Measure & Arc Length Remember: 𝒎 𝑪𝒆𝒏𝒕𝒓𝒂𝒍 ∠=𝒎 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕𝒆𝒅 𝑨𝒓𝒄 Arc Measure is in degrees; Arc Length is in units like cm, ft, and in. The central angle is a portion of the total degrees in a circle whereas Arc Length is a portion of the circumference. 𝑨𝒓𝒄 𝑴𝒆𝒂𝒔𝒖𝒓𝒆 𝟑𝟔𝟎 = 𝑨𝒓𝒄 𝑳𝒆𝒏𝒈𝒕𝒉 𝑪𝒊𝒓𝒄𝒖𝒎𝒇𝒆𝒓𝒆𝒏𝒄𝒆 Everything in circles is proportional!

Examples Find the arc length: 1. Radius 5 cm, central angle 50º Find the circumference: 3. Central angle 55º, arc length 5.5 cm 4. Central angle 60º, arc length 3.82 m Find the central angle: 5. Arc length 45 ft, radius 12 ft 6. Arc length 30in, radius 14 in

Classwork Homework Geometry book p. 686-688 #13-47 odd Circumference and Arc Length

Exit Ticket 1. How does a central angle compare to its intercepted arc? 2. What is the difference between arc length and arc measure? 3. What proportion can you use with respect to arc measure and arc length?