Chapter 10.3: Central Angles and Arcs Flashcards
Central Angle
an angle whose vertex is the center of a circle is a central angle of the circle.
Minor arc
on circle P, if measure of angle APB < 180 degrees, then the points A and B, together with the points of circle P that lie in the interior of angle APB, form a minor arc of the circle.
Measure of a minor arc
is defined to be the measure of its central angle.
Semicricle
if the endpoints of an arc are two endpoints of a diameter, then the arc is a semicircle and its measure is 180 degrees.
Major arc
on circle P, if measure of angle APB < 180 degrees, then the points A and B, together with the points of circle P that lie in the exterior of angle APB form a major arc of the circle.
Measure of a major arc
is defined to be the difference between 360 degrees and the measure of its associated minor arc.
Adjacent arcs
two arcs of the same circle are adjacent if they intersect at exactly one point.
Post. 21 - Arc Addition Post.
the measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.
Congruent arcs
on the same circle or on congruent circles, two arcs are congruent if and only if they have the same measure.
Thm. 10.4
in the same circle, or in congruent circles, two arcs are congruent if and only if their central angles are congruent.
