section 9-3 arcs and central angles. central angle an angle with its vertex at the center of a...
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Section 9-3Arcs and
Central Angles
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Central angle• An angle with its vertex at the center of a circle.
is a central angleABC
Circle B
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ARC• an unbroken part of a circle
AC : read “arc AC”
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Types of Arcs:1. Minor Arc: less than 180
• Measure is the same as its central angle• Named using two letters (Ex: )
2. Major Arc: more than 180• Measure is 360 minus the measure of its
central angle• Named using three letters (Ex: )
3. Semicircle: equals 180• Endpoints of a diameter • Named using three letters
PQR
AC
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Adjacent Arcs
• Arcs in a circle that have exactly one point in common.
D
CB
A
m AB = 90andm BD = 30are adjacent arcs
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Arc addition postulate
• The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs.
• Applies like segment addition postulate
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D
CB
A
m = m PQRm AB = 90PQ + m m BD = 30QR = m ABD
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Congruent Arcs• Arcs, in the same circle or in
congruent circles, that have equal measures.
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Theorem 9-3• In the same circle or in
congruent circles, two minor arcs are congruent if and only if their central angles are congruent.