Measuring Angles and Arcs

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Presentation transcript:

Measuring Angles and Arcs

Angles and Arcs Central angle Is an angle whose vertex is at the center of a circle and whose sides are radii

Angles and Arcs Sum of measures of central angles 1 3 2

Angles and Arcs An Arc A portion of circle defined by two endpoints R

Angles and Arcs R A central angle separates a circle into two arcs Q P Measures of the arcs are related to the measures of central angles

Angles and Arcs A Minor Arc x B C The shortest arc connecting two endpoints on a circle B Its measure is less than 180 C

Angles and Arcs A Major Arc x B C D The longest arc connecting two endpoints on a circle B Its measure is greater than 180 C D

Angles and Arcs A Semicircle D 180 B C Is an arc with endpoints that lies on a diameter B The measure of a semicircle is 180 C

Angles and Arcs F 1 2 H G Two minor arcs are congruent if and only if their corresponding central angles are congruent 2 H G

Angles and Arcs F Adjacent arcs H G