Transcript Arcs and Central Angles

Arcs and Central Angles
Lesson 9.3
Geometry Honors
Objective
Lesson Focus
A part of a circle is called an arc. Arcs can be associated with
angles whose vertices are at the center of circles.
The purpose of this lesson is to study arcs and central angles.
Arcs and Central Angles
central angle
an angle with its vertex at the center of the circle
minor arc
the smaller of the arcs created by a central angle
major arc
the larger of the arcs created by a central angle
semicircle
The two arcs that are cut off by a diameter.
Arcs and Central Angles
measure of a minor arc
the measure of the central angle of a minor arc
measure of a major arc
the measure of the central angle of a major arc
measure of a semicircle
the measure of a semicircle is 180
Arcs and Central Angles
adjacent arcs
arcs of a circle that have exactly one point in common
congruent arcs
arcs in the same circle or in congruent circles that have
equal measures
Arcs and Central Angles
Arc Addition Postulate
The measure of the arc formed by two adjacent arcs is
the sum of the measures of these two arcs.
Arcs and Central Angles
Theorem
In the same circle or in congruent circles, two minor arcs
are congruent if and only if their central angles are
congruent.
Written Exercises
Problem Set 9.3A, p.341: # 2 - 20 (even)