Document Sample

Bell work Find the value of radius, x, if the diameter of a circle is 25 ft. 25 ft x Bell work Answer Radius, x, is 12.5 ft Unit 3 : Circles: 10.2 Arcs and Chords Objectives: Students will: 1. Use properties of arcs and chords to solve problems related to circles. Words for Circles Check your answers to see how you did. 1. Central Angle 2. Minor Arc 3. Major Arc 4. Semicircle 5. Congruent Arcs 6. Chord 7. Congruent Chords Are there any words/terms that you are unsure of? Label Circle Parts 1. Semicircles 5. Exterior 9. Tangent 2. Center 6. Interior 10. Secant 3. Diameter 7. Diameter 11. Minor Arc 4. Radius 8. Chord 12. Major Arc Arcs of Circles CENTRAL ANGLE – An angle with its vertex at the center of the circle Central Angle A CENTER P • P • 60º • B Arcs of Circles Minor Arc AB and Major Arc ACB Central Angle A CENTER P • MINOR ARC P AB • 60º MAJOR ARC • • C B ACB Arcs of Circles The measure of the Minor Arc AB = the measure of the Central Angle The measure of the Major Arc ACB = 360º - the measure of the Central Angle Central Angle A CENTER P • Measure of the MINOR ARC = P the measure of the • 60º Central Angle The measure of the MAJOR ARC = 300º 360 – the measure of C • • AB = 60º B the MINOR ARC ACB = 360º - 60º = 300º Arcs of Circles Semicircle – an arc whose endpoints are also the endpoints of the diameter of the circle; Semicircle = 180º 180º • Semicircle Arc Addition Postulate The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs A • • C AB + BC = ABC 170º • 80º 170º + 8 0º = 2 5 0º ARC ABC = 250º •B Example 1 X • • Y 75º P• 110° • Z Arc Addition Postulate Answers: arcXY 75 arcYZ 110 arcXYZ 185 arcXZ 175 (p. 605) Theorem 10.4 In the same circle or in congruent circles two minor arcs are congruent iff their corresponding chords are congruent Congruent Arcs and Chords Theorem Example 1: Given that Chords DE is congruent to Chord FG. Find the value of x. Arc DE = 100º D E F G Arc FG = (3x +4)º Congruent Arcs and Chords Theorem Answer: x = 32º Arc DE = 100º D E F G Arc FG = (3x +4)º Congruent Arcs and Chords Theorem Example 2: Given that Arc DE is congruent to Arc FG. Find the value of x. D E Chord DE = 25 in Chord FG = (3x + 4) in F G Congruent Arcs and Chords Theorem Answer: x = 7 in D E Chord DE = 25 in Chord FG = (3x + 4) in F G (p. 605) Theorem 10.5 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chords and its arcs. Chord Diameter Congruent Arcs P • Congruent Segments (p. 605) Theorem 10.6 If one chord is the perpendicular bisector of another chord then the first chord is the diameter Chord 2 Chord 1: _|_ bisector of Chord 2, Chord 1 = the diameter P • Diameter (p. 606) Theorem 10.7 In the same circle or in congruent circles, two chords are congruent iff they are equidistant from the center. (Equidistant means same perpendicular distance) Q T V Chord TS Chord QR __ __ • R iff PU VU U P S Center P Example Find the value of Chord QR, if TS = 20 inches and PV = PU = 8 inches Q T V 8 in • R U P 8 in S Center P Answer Chord QR = 20 inches (Theroem 10.7) Home work PWS 10.2 A P. 607- 608 (12-46) even Journal Write two things about Arcs and Chords related to circles from this lesson.

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 0 |

posted: | 2/28/2012 |

language: | |

pages: | 24 |

OTHER DOCS BY wanghonghx

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.