Central Angles and Arc Measures

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ARCS AND CENTRAL ANGLES

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Presentation transcript:

Central Angles and Arc Measures Advanced Geometry

CENTRAL ANGLE An angle whose vertex is the center of a circle is a central angle.

ARC OF A CIRCLE A section of the circumference of a circle is an arc.

MINOR VS MAJOR MINOR ARC – If the measure of a central angle is less than 180 degrees, then the arc formed by that central angle is a minor arc. MAJOR ARC – If the measure of a central angle is greater than 180 degrees, then the arc formed by that central angle is a major arc.

SEMICIRCLE If the endpoints of an arc are the endpoints of a diameter, then the arc is a semicircle.

Naming Arcs Minor Arc Major Arc Semicircle

Example

ARC ADDITION POSTULATE The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Measuring Arcs The measure of a minor arc is defined to be the measure of its central angle.

CONGRUENT ARCS Two arcs of the same circle or of congruent circles are congruent arcs if they have the same measure. central angles are congruent

Example

Example Find the measure of arc DE.