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Chapter 7: Area Lesson 7-6: Circles and Arcs

Chapter 7: Area Lesson 7-6: Circles and Arcs. Goals : Find the measures of central angles and arcs. Find circumference and arc length.  and the law :.

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Chapter 7: Area Lesson 7-6: Circles and Arcs

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  1. Chapter 7: AreaLesson 7-6: Circles and Arcs Goals: Find the measures of central angles and arcs. Find circumference and arc length.

  2.  and the law: • In 1896, an Indiana physician promoted a legislative bill that made  equal to 3.2 exactly. The Indiana House of Representatives approved the bill unanimously, 67 to 0. The Senate, however, deferred debate about the bill “until a later date.” • From A Passion for Mathematics, by Clifford A. Pickover.

  3. Circles: • circle: In a plane, a circle is the set of all points equidistant from a given point called the center. We name a circle by its center. • A radius is a segment that has one endpoint at the center and the other endpoint on the circle. Congruent circles have congruent radii. • A diameter is a segment that contains the center of a circle and has both endpoints on the circle. • A central angle is an angle whose vertex is the center of the circle.

  4. Arcs and their measures: • An arc is a part of a circle. One type of arc, a semicircle, is half of a circle. A minor arc is smaller than a semicircle. A major arc is greater than a semicircle. Adjacent arcs are arcs of the same circle that have exactly one point in common. • The measure of a semicircle is 180°. The measure of a minor arc is the measure of its corresponding central angle. The measure of a major arc is 360° minus the measure of its related minor arc.

  5. Arc Addition Postulate: • Postulate 7-1 – Arc Addition Postulate: The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs: mABC = mAB + mBC.

  6. Circumference and Concentric Circles: • Theorem 7-13 – Circumference of a Circle: The circumference of a circle is  times the diameter: C = d or C = 2r. • Concentric circles: Circles that lie in the same plane and have the same center are concentric circles.

  7. Arc Length and Congruent Arcs: • Arc Length: The measure of an arc is in degrees, while the arc length is a fraction of a circle’s circumference. • Theorem 7-14 – Arc Length: The length of an arc of a circle is the product of the ratio (measure of the arc)/360 and the circumference of the circle. • Congruent Arcs: Congruent arcs are arcs that have the same measure and are in the same circle or in congruent circles.

  8. Assignments and Note: • CW: Practice 7-6. • HW 7-6: #3-39 (every 3rd); #60 is extra credit. • Test on Friday.

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