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Chapter 10 : Circles

This chapter delves into the definitions and measurements of arcs in a circle. It defines central angles, minor arcs, major arcs, and semicircles, emphasizing that arcs are measured in degrees, correlating their measures with central angles. Additionally, it introduces the concept of circle congruency, stating that two circles are congruent if their radii are equal. The chapter includes problems to help reinforce understanding of these concepts, challenging students to find the measures of various arcs and values that ensure circle congruency.

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Chapter 10 : Circles

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  1. Chapter 10: Circles 10.2.1 Find Arc Measures

  2. Definitions • Central Angle – of a circle is an angle whose vertex is the center of a circle • Minor Arc – of a circle is a set of points between two given points of a circle • Major Arc – of a circle is a set of points that do not lie on the minor arc • Arcs are measured in degrees • Measure of the arc is equal to the measure of the central angle • Semicircle – is when the major and minor arc are congruent (180⁰) AB mAB = mACB ADB A C 50⁰ 50⁰ D mADB = 360⁰ - mAB B

  3. Find the Measure of each arc • AB c) ABD • AD A 50⁰ B C D

  4. Circle Congruency (definition) • Two circles are congruent if they have congruent radii • Find the value of x so that circle A is congruent to circle D 110 A x 2 + 10 D

  5. Find the Value of x and y so that circle C is congruent to circle H E (-3x +6y)⁰ A F B H C 6x+8 y G D

  6. Homework • p. 661 • 1, 2, 4 – 10even, 11 – 25 odd, 26 – 34 even

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