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Explore Central and Minor Arc Measures in Circles

Learn about central angles, arcs, minor and major arcs, semicircles, and how to find arc measures. Understand the Arc Addition Postulate and the concept of congruent arcs in circles.

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Explore Central and Minor Arc Measures in Circles

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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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