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Lesson 10-2 Angles and Arcs

Lesson 10-2 Angles and Arcs. •Recognize major arcs, minor arcs, semicircles, and central angles and their measures •Find arc length. Central Angle. An angle with the center of the circle as its vertex, and its sides contain two radii of the circle.

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Lesson 10-2 Angles and Arcs

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  1. Lesson 10-2Angles and Arcs •Recognize major arcs, minor arcs, semicircles, and central angles and their measures •Find arc length.

  2. Central Angle • An angle with the center of the circle as its vertex, and its sides contain two radii of the circle. • The sum of the measure of the central angles of a circle with no interior points in common is 360°.

  3. Arc • A part of a circle that is defined by two endpoints. • The measure of an arc is the same as the measure of its central angle.

  4. Minor arc

  5. Major Arc

  6. Semicircle • An arc that measures 180°. • A semicircle is named by the two endpoints and another point on the arc.

  7. Theorem 10.1 • In the same or in congruent circles, two arcs are congruent if and only if their corresponding central angles are congruent.

  8. Adjacent arcs • Arcs of a circle that have exactly one point in common.

  9. Postulate 10.1 – Arc Addition Postulate • The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. • In OS, mPQ + mQR = mPQR.

  10. Arc Length Formula

  11. Assignment pg. 533 #14-41, 47-50

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