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6.2 Find Arc Measures

6.2 Find Arc Measures. Vocabulary. A central angle of a circle is an angle whose vertex is the center of the circle. A semicircle is an arc with endpoints that are the endpoints of a diameter. Vocabulary. An arc is an unbroken part of a circle.

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6.2 Find Arc Measures

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  1. 6.2Find Arc Measures

  2. Vocabulary • A central angle of a circle is an angle whose vertex is the center of the circle. • A semicircle is an arc with endpoints that are the endpoints of a diameter.

  3. Vocabulary • An arc is an unbroken part of a circle. • A minor arc is an arc of a circle having measure less than 180o • A major arc is an arc of a circle having measure greater than 1800 • What would we call an arc that equals 180o?

  4. Vocabulary • The measure of a minor arc is the measure of its central angle. • The measure of a major arc is the difference between 360o and the measure of the related minor arc.

  5. Vocabulary • Arc Addition Postulate • The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. • Congruent Circles are two circles with the same radius. • Congruent arcs are two arcs with the same measure that are arcs of the same circle or of congruent circles.

  6. Example 1: • Find the measure of each arc of circle J, where KM is a diameter. • Arc LM • Arc LKM • Arc LK • Arc KLM

  7. Example 2: • Several students were recently asked about their favorite color. The results are shown in the graph. Find the indicated arc measures. • Arc RT • Arc PRT • Arc RTQ • Arc STQ

  8. Example 3: • Tell whether the highlighted arcs are congruent. Explain why or why not.

  9. Homework • P. 193 #1-18, 32-35

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