valuate: Homework and Practice Identify the chord (s), inscribed angle (s), and central angle (s) in the figure. The center of the circles in xercises 1, 2, and 4 is. Online Homework Hints and Help xtra Practice 1. 2. S T R U hord(s): Inscribedngle(s): entral ngle(s): hord(s): Inscribed ngle(s): entral ngle(s): 3. 4. G hord(s): Inscribed ngle(s): hord(s): Inscribed ngle(s): entral ngle(s): entral ngle(s): In circle, m = 84. ind each measure. 5. m G 6. m H 84 G Houghton Mifflin Harcourt Publishing ompany Module 15 786 Lesson 1
The center of the circle is. ind each measure using the appropriate theorems and postulates. 7. m 51 8. m 9. m ind each measure using the appropriate theorems and postulates. m = 116 10. m 116 28 70 11. m Houghton Mifflin Harcourt Publishing ompany The center of the circle is. ind each measure using the appropriate theorems and postulates. m LM = 70 and m NP = 60. 12. m MNP 13. m LMN 70 L M P 60 N Module 15 787 Lesson 1
The center of the circle is O. ind each arc or angle measure using the appropriate theorems and postulates. 14. m 15. m 48 70 O 16. m 17. m Represent Real-World Problems The circle graph shows how a typical household spends money on energy. Use the graph to find the measure of each arc. 18. m PQ 19. m UPT Heating and cooling 45% Q R Water heater 11% Home nergy Use P Others 19% V Lighting U 7% Washer and dryer 10% T ishwasher S 2% Refrigerator 6% Houghton Mifflin Harcourt Publishing ompany Module 15 788 Lesson 1
20. ommunicate Mathematical Ideas carpenter s square is a tool that is used to draw right angles. Suppose you are building a toy car and you have four small circles of wood that will serve as the wheels. You need to drill a hole in the center of each wheel for the axle. xplain how you can use the carpenter s square to find the center of each wheel. 6 19 4 5 20 3 4 21 2 3 22 1 arpenter s square 2 23 1 0 1 2 3 4 5 1 2 3 4 5 6 7 21. hoose the expressions that are equivalent to m O. Select all that apply.. 2 m. m O. m. m. 2m. m G. 2m H. m O Houghton Mifflin Harcourt Publishing ompany Zoran Zeremski/ Shutterstock 22. nalyze Relationships raw arrows to connect the concepts shown in the boxes. Then explain how the terms shown in the concept map are related. hord entral ngle rc Inscribed ngle Inscribed ngle of a iameter Module 15 789 Lesson 1
23. In circle, the measures of,, and are in the ratio 3:4:5. ind m. H.O.T. ocus on Higher Order Thinking 24. xplain the rror The center of the circle is G. elow is a student s work to find the value of x. xplain the error and find the correct value of x. _ is a diameter, so m = 180. Since m = m + m + m, m + m + m = 180. 5x + 90 + 15x = 180 20x = 90 x = 4.5 (16x - 5) 5x G 15x 25. Multi-Step n inscribed angle with a diameter as a side has measure x. If the ratio of m to m is 1:4, what is m? x 26. Justify Reasoning To prove the Inscribed ngle Theorem you need to prove three cases. In ase 1, the center of the circle is on a side of the inscribed angle. In ase 2, the center the circle is in the interior of the inscribed angle. In ase 3, the center the circle is in the exterior of the inscribed angle. a. ill in the blanks in the proof for ase 1 to show that m = 2 m. Given: is inscribed in circle. Prove: m = 2 m Proof: Let m = x. raw _. is. So m = m by the Isosceles Triangle Theorem. Houghton Mifflin Harcourt Publishing ompany Then = 2x by the xterior ngle Theorem. So, m = the definition of the measure of an arc of a circle. by Since m = and m =, m = 2. Module 15 790 Lesson 1
b. raw and label a diagram for ase 2. Then use a paragraph proof to prove that the inscribed angle is one-half the intercepted arc. c. raw and label a diagram for ase 3. Then use a paragraph proof to prove that the inscribed angle is one-half the intercepted arc. Houghton Mifflin Harcourt Publishing ompany Module 15 791 Lesson 1
Lesson Performance Task iana arrives late at the theater for a play. Her ticket entitles her to sit anywhere in ircle G. She had hoped to sit in Seat, which she thought would give her the widest viewing angle of the stage. ut Seat is taken, as are all the other nearby seats in ircle G. The seating chart for the theater is shown. ircle K ircle G ircle Stage Identify two other spots where iana can sit that will give her the same viewing angle she would have had in Seat. xplain how you know how your points would provide the same viewing angle, and support your claim by showing the viewing angles on the drawing. Houghton Mifflin Harcourt Publishing ompany Module 15 792 Lesson 1