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10.2 Find Arc Measures

10.2 Find Arc Measures. Central Angle – an angle whose vertex is the center of a circle. A. C. B. Central Angles.  ACB is a central angle. Arcs. Arc - a piece of a circle. - named with 2 or 3 letters - measured in degrees

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10.2 Find Arc Measures

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  1. 10.2 Find Arc Measures

  2. Central Angle – an angle whose vertex is the center of a circle A C B Central Angles ACB is a central angle

  3. Arcs Arc - a piece of a circle. - named with 2 or 3 letters - measured in degrees Minor Arc - part of a circle that measures less than 180o (named by 2 letters). A B B ( BP P

  4. More Arcs Major Arc - part of a circle that measures between 180o and 360o. Named with three letters Semicircle – an arc whose endpoints are the endpoints of a diameter of the circle (or ½ of a circle) CPS A B ( ( ABC or CBA C C P ( S

  5. Arc Measures Measure of a Minor Arc – equals the measure of its central angle Measure of a Major Arc – equals 360o minus the measure of the minor arc

  6. example: find the arc measures ( m AB = m BC = m AEC = m BCA 50o E ( 130o ( 180o A 180o ( 50o =180o+130= 310o 130o C or 360o - 50o = 310o B

  7. Arc Addition Postulate The measure of an arc formed by two adjacent arcs is the sum of the measures of those arcs. B A C ( ( ( m AB + m BC = mABC

  8. Congruency Among Arcs Congruent Arcs - 2 arcs with the same measure and the same length They MUST be from the same circle or  circles!!!

  9. Example ( m AB = 30o ( A m DC = 30o ( ( AB  DC 30o E B D 30o C

  10. example continued ( mBD = 45o A ( mAE = 45o B ( ( BD  AE 45o The arcs are the same measure; so, why aren’t they ? C D E The 2 circles are NOT  !

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