Arcs and Central Angles Lesson 9.3 Geometry Honors

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Arcs and Central AnglesLesson 9.3Geometry
Honors

• Objective

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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.

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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.

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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?

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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

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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.

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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.

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Written Exercises

• Problem Set 9.3A, p.341 2 - 20 (even)