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.

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ARCS AND CENTRAL ANGLES

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Presentation transcript:

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. A minor arc is an arc of a circle having measure less than 180 o A major arc is an arc of a circle having measure greater than What would we call an arc that equals 180 o ?

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

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.

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

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

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

Homework P. 193 #1-18, 32-35