10.2 Arc Measures.

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Presentation transcript:

10.2 Arc Measures

The two points are called endpoints Arc Two points on the circle and a continuous (unbroken) part of the circle between the two points The two points are called endpoints

Semicircle An arc of a circle whose endpoints are the endpoints of a diameter; HALF of a circle Minor Arc An arc of a circle that is smaller than a semicircle Major Arc An arc of a circle that is larger than a semicircle

Semicircles & Major arcs uses 3 letters Naming an Arc arc AB is written as Minor arcs use 2 letters Semicircles & Major arcs uses 3 letters

Central Angle A central angle has its vertex at the center of the circle. Central Angles Not Central Angles

Has the same measure as the central angle that intercepts it Arcs Two points on the circle and a continuous (unbroken) part of the circle between the two points. Measured in Degrees – 360 around the circle Has the same measure as the central angle that intercepts it

Congruent Chords Conjecture Given: Marked Info Prove: The arcs intercepted by the chords are congruent Hint: Do not use vertical angles. (Why?)

Two arcs have equal measures if and only if their circles are congruent and their central angles are congruent.