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10.2 Angles and Arcs

10.2 Angles and Arcs. What you’ll learn: To recognize major arcs, minor arcs, semicircles, and central angles and their measures. To find arc length. Central angles. Central angle – an angle whose vertex is at the center of a circle with sides that are radii of the circle.

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10.2 Angles and Arcs

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  1. 10.2 Angles and Arcs What you’ll learn: To recognize major arcs, minor arcs, semicircles, and central angles and their measures. To find arc length.

  2. Central angles Central angle – an angle whose vertex is at the center of a circle with sides that are radii of the circle. Sum of central angles – the sum of the measures of the central angles of a circle with no interior points in common is 360. 1+2+3=360 1 2 3

  3. Arcs Arcs are created by central angles. An arc is a piece of a circle. Their measure is directly related to the measure of the central angle that creates the arc. Symbol Three kinds of arcs: Minor arc – measure is less than 180 degrees. Named by 2 letters that are the endpoints. Major arc – measure is more than 180 degrees Named by 3 letters where the 1st and 3rd letters are the endpoints of the arc. Semicircle – measure is 180 degress. Named by 3 letters where the 1st and 3rd letters are the endpoints of the arc. B E C A D

  4. Theorems/Postulates Theorem 10.1 In the same or in congruent circles, two arcs are congruent iff their corresponding central angles are congruent. if ADBBDC and vice-versa. Postulate 10.1 Arc Addition Postulate The measure of an arc formed by 2 adjacent arcs is the sum of the measures of the 2 arcs. WZX+XZY=WZY A D B C W X Z Y

  5. RV is a diameter of T. R • Find mRTS • Find mQTR Q S (8x-4) (13x-3) T 20x (5x+5) U V

  6. In P, mNPM=46, PL bisects KPM, and OPKN. Find each measure. 1. 2. 3. L K M P J O N

  7. Arc Length Arc length is the actual measure of an arc. It is a fractional part of the circumference. You must know 2 things in order to find arc length: the radius (or diameter) and the arc measure (in degrees). Use the following formula to find arc length ( ) where A=arc measure or Example: Find A 72 C B 7 in

  8. Homeworkp. 53314-42 even

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