Warm – up Find the radius of the circle given the picture below.

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Warm – up Find the radius of the circle given the picture below.

Arc Measure Section 6.2

Standards MM2G3. Students will understand the properties of circles. c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector. d. Justify measurements and relationships in circles using geometric and algebraic properties.

Essential Questions What are the important circle measurements?

Vocabulary Central angle – an angle whose vertex is the center of the circle central angle

Semicircle – an arc with endpoints that are the endpoints of a diameter.

Arcs An arc is a unbroken part of a circle Types of arcs Minor arc- the measure of the arc is less than 180° Major Arc – the measure of the arc length is greater than 180 °

Diagram of Arcs

Example 1 Name the major and minor arcs of the given circle G.

Measure of Arcs Measure of a minor arc - is the measure of the central angle. Measure of a major arc - is the difference between 360° and the measure of the related minor arc.

Arc Addition Postulate The measure of an arc formed by two adjacent arcs is the sum of the measure of the two arcs.

Example 2 Find the measure of the following

You Try!! Find the measure of each arc. 70° 360° - 70° = 290° 180°

Vocabulary Congruent Circles – are two circles with the same radius. Congruent Arcs – two arcs with the same measure that are arcs of the same circle or congruent circles.

Example 2 Find the measures of the red arcs. Are the arcs congruent?

Example 3 Find the measures of the red arcs. Are the arcs congruent?

Homework Page 193 - 194 2 – 38 even