Arcs and Central Angles

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ARCS AND CENTRAL ANGLES

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Presentation transcript:

Arcs and Central Angles Section 9-3: Arcs and Central Angles

1. central angle: an angle with its ___________ _______________________________________ 2. arc: an ______________________________ 3. ________ is an arc measuring less than half the circle. (Use 2 letters when naming). vertex at the center of the circle. unbroken part of a circle. Minor

4. ________ is an arc measuring more than half the circle 4. ________ is an arc measuring more than half the circle. (Use 3 letters when naming). 5. ____________ is an arc measuring exactly 180° or half the circle. (Use 3 letters when naming). 6. If C and B are the endpoints of a diameter, then the two arcs are called ____________. Major Semicircles semicircles

7. List examples of minor arcs: ______________ 8 7. List examples of minor arcs: ______________ 8. List examples of major arcs: ______________ ____________________ 9. List examples of semi-circles: _____________ 𝐴𝐵 , 𝐵𝐷 , 𝐷𝐶 , 𝐶𝐴 𝐴𝐵𝐶 , 𝐴𝐷𝐶 , 𝐵𝐷𝐴 , 𝐵𝐶𝐴 𝐶𝐴𝐵 , 𝐵𝐷𝐶

10. _____________ are arcs that have exactly one point in common 10. _____________ are arcs that have exactly one point in common. They do not overlap. 11. List examples of adjacent arcs: _________________________________ 12. _______________ are arcs, in the same circle or in congruent circles, that have equal measures. Adjacent arcs 𝐴𝐵 𝑎𝑛𝑑 𝐵𝐷 ; 𝐵𝐷𝐶 and 𝐶𝐴 Congruent arcs

Postulate 16 – Arc Addition Postulate The measure of the arc formed by two ___________ arcs is the _____ ___ ______ ___________ ___ ______ _____ _____. adjacent sum of the measures of these two arcs

* The measure of a minor arc is the measure of its central angle. 13. m 𝐴𝐵 = _____ 14. m 𝐶𝐴𝐵 = _____ 15. m 𝐴𝐶 = _____ 16. m 𝐶𝐷𝐵 = _____ 17. mAOC = _____ 18. mBOC = _____ 19. m 𝐴𝐶𝐵 = _____ 20. m 𝐴𝐵𝐶 = _____ 60° 180° 120° 180° 120° 180° 300° 240° 120° 60° 120°

130° 72° 50°

150° 30° 150° 95°

4x = 4(26) = 104 2x – 14 = 2(26) – 14 = 38 2x = 2(26) = 52 38 3x + 10 = 3(26) + 10 = 88 104 52 3x = 3(26) = 78 88 78 4x + 2x – 14 + 2x + 3x + 10 + 3x = 360 14x – 4 = 360 14x = 364 x = 26

= 88⁰ = 52⁰ = 38⁰ = 104⁰ = 78⁰ = 166⁰ = 322⁰

HOMEWORK: page 341 #1-13 all (CE)