Chapter 10.3: Central Angles and Arcs Flashcards

1
Q

Central Angle

A

an angle whose vertex is the center of a circle is a central angle of the circle.

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2
Q

Minor arc

A

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.

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3
Q

Measure of a minor arc

A

is defined to be the measure of its central angle.

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4
Q

Semicricle

A

if the endpoints of an arc are two endpoints of a diameter, then the arc is a semicircle and its measure is 180 degrees.

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5
Q

Major arc

A

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.

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6
Q

Measure of a major arc

A

is defined to be the difference between 360 degrees and the measure of its associated minor arc.

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7
Q

Adjacent arcs

A

two arcs of the same circle are adjacent if they intersect at exactly one point.

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8
Q

Post. 21 - Arc Addition Post.

A

the measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

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9
Q

Congruent arcs

A

on the same circle or on congruent circles, two arcs are congruent if and only if they have the same measure.

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10
Q

Thm. 10.4

A

in the same circle, or in congruent circles, two arcs are congruent if and only if their central angles are congruent.

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