Transcript ARCS - SCEVMATH.ORG

10.2 Arc Measures
Arc
A
B
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
B
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
A
A
C
B
A
B
Naming an Arc
arc AB is written as AB
Minor arcs use 2 letters
A
Semicircles & Major arcs
uses 3 letters
B
C
B
ACB
A
Central Angle
A central angle has its vertex at the center of
the circle.
Central Angles
Not Central Angles
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.