Riding a Ferris Wheel. Students should be able to answer these questions after Lesson 10.1:

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1 .1 Riding a Ferris Wheel Introduction to ircles Students should be able to answer these questions after Lesson.1: What are the parts of a circle? How are the parts of a circle drawn? Read Question 1 and its solution. Then draw an example of each vocabulary term in Question Identify the following in the circle below: center: O radius: O chord: secant: F point of tangency: central angle: O inscribed angle: arc: minor arc: major arc: F F 2. Using the circle below, draw and properly label an example of each of the following. F O center radius chord diameter secant tangent point of tangency central angle inscribed angle arc semicircle minor arc major arc hapter Homework Helper 69

2 .2 Holding the Wheel entral ngles, Inscribed ngles, and Intercepted rcs Students should be able to answer these questions after Lesson.2: How is the measure of an arc determined? How is the measure of an inscribed angle determined? How is the measure of a central angle determined? 1. m 50º m º m º Step 1 Step 2 The measure of an intercepted arc is equal to the measure of the central angle, so m 50º. The measure of an inscribed angle is half the measure of the intercepted arc, so m m 70º 3. m RIH 45º m K º m L º 70 K L m RH º m RH º R H 45 I 70 hapter Homework Helper

3 .3 anhole overs easuring ngles Inside and Outside of ircles Students should be able to answer these questions after Lesson.3: How is the measure of an angle formed by two chords determined? How is the measure of an angle formed by two secants determined? How is the measure of an angle formed by a secant and a tangent determined? How is the measure of an angle formed by two tangents determined? Read Question 1 through 4 and their solutions. Then complete Questions 5 through L 2. m F 50º I H m ILH 180º K m FK º F O N K m 1º m ON 20º m K º Step 1 m FK 115º Step 1 2 m K º 3. T 4. S R Q P Z m SQ 40º m SP 175º m SRQ º Step 1 m SRQ 67.5º Step 1 m UVX 2 Y U V X W m UYX 300º m UX 60º m UVX º º hapter Homework Helper 71

4 5. F 6. L m F 280º H I m HI 0º m 80º m º K m K º m HI º 7. R 8. X Q P O N m PN 70º m QRN 200º m PN º S U T V W m UV 60º m SXW 180º m STW º 72 hapter Homework Helper

5 .4 olor Theory hords and ircles Students should be able to answer these questions after Lesson.4: What is the relationship between the chord and the diameter of a circle? What is the relationship between congruent chords and their minor arcs? F 1. a. If, what conclusions can be drawn about the arcs of the circle above? Step 1 If two chords in a circle are congruent, then their corresponding minor arcs are congruent. If, then you know that. b. If and is the center of the circle, what conclusions can be drawn from the circle above? Step 1 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. If you know that, you can also conclude that. 2. In the circle shown at the right, m 80º and. Find m. F 3. In the circle shown at the right, and is the center of the circle. Is? Use complete sentences in your answer. hapter Homework Helper 73

6 .5 Solar clipses Tangents and ircles Students should be able to answer these questions after Lesson.5: What is the relationship between a tangent line and a radius? What is the relationship between congruent tangent segments? 1. In the figure shown below, F centimeters. Find F, m HF, and m HF. H F Step 1 If two tangent segments to a circle are drawn from the same point outside the circle, then the tangent segments are congruent. F centimeters. Step 2 tangent to a circle is perpendicular to the radius that is drawn to the point of tangency. So, m HF m HF 90º. 2. m NQ º QN QP Q 3. xplain how the SS ongruency Theorem can be used to show that, in the figure at the left, QN QP. Use complete sentences in your answer. P N 74 hapter Homework Helper

7 .6 ears rc Length Students should be able to answer this question after Lesson.6: How is the length of an arc determined? 1. The radius of a circle is 5 centimeters. Find the circumference. Step 1 ircumference is the distance around a circle. The formula for circumference is d, where d is the diameter of the circle. If the radius is 5 centimeters then the diameter is centimeters. centimeters 2. The diameter of a circle is 6 centimeters. Find the circumference. 3. The radius of a circle is 7 centimeters. Find the circumference. Read Question 4 and its solution. Then complete Question The radius of circle T is 7 centimeters and m RTS 0º. Find the arc length of RS. R S T Step 1 Find the circumference. 14 centimeters. Step 2 ecause m RTS 0º and RTS is a central angle, m RS 0º. The arc length of 0º 35 RS is 14, or centimeters. 360º 9 5. The radius of circle V is centimeters and m WVU 130º. Find the m WU. W V U hapter Homework Helper 75

8 .7 Playing arts reas and Parts of ircles Students should be able to answer these questions after Lesson.7: How is the area of a sector determined? How is the area of a segment determined? 1. In the figure shown below, m Z 90º and the radius is 5 centimeters. Find the area of the sector. Z Step 1 alculate the area of the entire circle. r 2 (5) 2 25 square centimeters. Step 2 Find the portion of the circle contained by the sector. 90º 360º 1 4 Find the area of the sector. ( 1 4 ) (25 ) 6.25 The area of the sector is 6.25 square centimeters. 2. In the figure shown below, m Z 0º 3. In the figure shown below, m 120º and the radius is 8 centimeters. Find the and the radius is 2 centimeters. Find the area of the sector. area of the sector. Z 76 hapter Homework Helper