# Replacement for a Carpenter s Square

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1 Lesson.1 Skills Practice Name Date Replacement for a arpenter s Square Inscribed and ircumscribed Triangles and Quadrilaterals Vocabulary nswer each question. 1. How are inscribed polygons and circumscribed polygons different? 2. Describe how you can use the Inscribed Right Triangle Diameter Theorem to show an inscribed triangle is a right triangle. 3. What does the onverse of the Inscribed Right Triangle Diameter Theorem help to show in a circle? 4. What information about a quadrilateral inscribed in a circle does the Inscribed Quadrilateral pposite ngles Theorem give? hapter Skills Practice 777

2 Lesson.1 Skills Practice page 2 Problem Set Draw a triangle inscribed in the circle through the three points. Then determine if the triangle is a right triangle No. The triangle is not a right triangle. None of the sides of the triangle is a diameter of the circle hapter Skills Practice

3 Lesson.1 Skills Practice page 3 Name Date Draw a triangle inscribed in the circle through the given points. Then determine the measure of the indicated angle. 9. In, m Determine m. m In, m Determine m. hapter Skills Practice 779

4 Lesson.1 Skills Practice page In, m Determine m. 12. In, m Determine m. 13. In, m Determine m. 14. In, m Determine m. 780 hapter Skills Practice

5 Lesson.1 Skills Practice page 5 Name Date Draw a quadrilateral inscribed in the circle through the given four points. Then determine the measure of the indicated angle. 15. In quadrilateral D, m Determine m D. D m D In quadrilateral D, m Determine m. D 17. In quadrilateral D, m Determine m D. D hapter Skills Practice 781

6 Lesson.1 Skills Practice page In quadrilateral D, m D Determine m. D 19. In quadrilateral D, m Determine m. D 20. In quadrilateral D, m 5 1. Determine m D. D 782 hapter Skills Practice

7 Lesson.1 Skills Practice page 7 Name Date onstruct a circle inscribed in each polygon hapter Skills Practice 783

8 Lesson.1 Skills Practice page hapter Skills Practice

9 Lesson.1 Skills Practice page 9 Name Date 26. reate a proof to prove each statement. 27. Given: Inscribed in circle, m 5 40, and m Prove: is a diameter of circle Statements Reasons 1. m 5 40, m Given 2. m 1 m 1 m rc ddition Postulate m Substitution 4. m Subtraction Property of Equality 5. m 5 2 m 5. Definition of inscribed angle 6. m Substitution 7. is a right triangle with right angle. 7. Definition of right triangle 8. is the diameter of circle. 8. onverse of Inscribed Right Triangle- Diameter Theorem hapter Skills Practice 785

10 Lesson.1 Skills Practice page 28. Given: Inscribed RST in circle with diameter RS, and m RT 5 60 Prove: m ST R S 60 T 786 hapter Skills Practice

11 Lesson.1 Skills Practice page 11 Name Date 29. Given: Inscribed quadrilateral D in circle, m 5 50, and m 5 90 Prove: m D hapter Skills Practice 787

12 Lesson.1 Skills Practice page Given: Inscribed quadrilateral MNPQ in circle, m MQ 5 75, and m NMQ Prove: m MN M 120 N Q P 788 hapter Skills Practice

13 Lesson.1 Skills Practice page 13 Name Date 31. Given: m 5 50, m 5 90, and m D 5 90 Prove: m D 5 90 D hapter Skills Practice 789

14 Lesson.1 Skills Practice page Given: D and D are supplementary angles Prove: m D 5 m D 790 hapter Skills Practice

15 Lesson.2 Skills Practice Name Date Gears rc Length Vocabulary Define the key term in your own words. 1. arc length 2. radian Problem Set alculate the ratio of the length of each arc to the circle s circumference. 1. The measure of is 40º º 360º 9 1 The arc is of the circle s 9 circumference. 2. The measure of D is 90º. 3. The measure of EF is 120º. 4. The measure of GH is 150º. 5. The measure of IJ is 5º. 6. The measure of KL is 75º. hapter Skills Practice 791

16 Lesson.2 Skills Practice page 2 Write an expression that you can use to calculate the length of RS. You do not need to simplify the expression. 7. R 8. R in. S 13 cm S ? 2p(15) R cm. 160 R 28 cm S S 11. R 12. R ft 33 yd S S alculate each arc length. Write your answer in terms of. 13. If the measure of is 45º and the radius is 12 meters, what is the arc length of? 5 2p(12) 5 24p Fraction of : 45º º 8 1 rc length of : (24p) 5 3p 8 The arc length of is 3p meters. 792 hapter Skills Practice

17 Lesson.2 Skills Practice page 3 Name Date 14. If the measure of D is 120º and the radius is 15 centimeters, what is the arc length of D? 15. If the measure of EF is 60º and the radius is 8 inches, what is the arc length of EF? 16. If the measure of GH is 30º and the radius is 6 meters, what is the arc length of GH? 17. If the measure of IJ is 80º and the diameter is centimeters, what is the arc length of IJ? hapter Skills Practice 793

18 Lesson.2 Skills Practice page If the measure of KL is 15º and the diameter is 18 feet, what is the arc length of KL? 19. If the measure of MN is 75º and the diameter is 20 millimeters, what is the arc length of MN? 20. If the measure of P is 165º and the diameter is 21 centimeters, what is the arc length of P? alculate each arc length. Write your answer in terms of. 21. If the measure of is 135º, what is the arc length of? 16 cm 5 2p(16) 5 32p Fraction of : 135º 360º 8 3 rc length of : 8 (32p) 5 96 p 5 12p 8 The arc length of is 12p cm hapter Skills Practice

19 Lesson.2 Skills Practice page 5 Name Date 22. If the measure of D is 45º, what is the arc length of D? 18 cm D 23. If the measure of EF is 90º, what is the arc length of EF? E 30 in. F hapter Skills Practice 795

20 Lesson.2 Skills Practice page If the measure of GH is 120º, what is the arc length of GH? G 27 in. H 25. If the length of the radius is 4 centimeters, what is the arc length of IJ? I 160 J 796 hapter Skills Practice

21 Lesson.2 Skills Practice page 7 Name Date 26. If the length of the radius is 7 centimeters, what is the arc length of KL? K L If the length of the radius is 11 centimeters, what is the arc length of MN? M 0 N hapter Skills Practice 797

22 Lesson.2 Skills Practice page If the length of the radius is 17 centimeters, what is the arc length of P? 75 P Use the given information to answer each question. Where necessary, use 3.14 to approximate. 29. Determine the perimeter of the shaded region. 30 mm 60 rc length: (3.14)(30) mm 360 Perimeter of shaded region: mm 798 hapter Skills Practice

23 Lesson.2 Skills Practice page 9 Name Date 30. Determine the perimeter of the figure below. 15 cm 30 cm semicircular cut was taken from the rectangle shown. Determine the perimeter of the shaded region. 80 ft 60 ft 32. circle has a circumference of 81.2 inches. What is the radius of the circle? hapter Skills Practice 799

24 Lesson.2 Skills Practice page 33. ella used a tape measure and determined the circumference of a flagpole to be 6.2 inches. What is the radius of the flagpole? 34. arla used a string and a tape measure and determine the circumference of a circular cup to be inches. What is the radius of the cup? Solve for each measure given the information. 35. If = s p and r 5 3, what is the length of the intercepted arc? 3 5 r p 3 5 s 3 s 5 p 36. If r 5 8 and the intercepted arc length is 6p, what is the measure of the central angle? 37. The measure of a central angle is 80. The length of the radius is 40 mm. Determine the arc length using the formula measure of angle 2pr hapter Skills Practice

25 Lesson.2 Skills Practice page 11 Name Date 38. If r 5 6 and the intercepted arc length is 4p, what is the measure of the central angle? 39. The measure of a central angle is 80. The length of the radius is 40 mm. Determine the arc length using the formula measure of angle? 2pr The measure of a central angle is 1. The length of the radius is 15 ft. Determine the arc length using the formula measure of angle? 2pr. 360 hapter Skills Practice 801

26 802 hapter Skills Practice

27 Lesson.3 Skills Practice Name Date Playing Darts Sectors and Segments of a ircle Vocabulary Draw an example of each term. 1. concentric circles 2. sector of a circle 3. segment of a circle hapter Skills Practice 803

28 Lesson.3 Skills Practice page 2 Problem Set alculate the area of each sector. Write your answer in terms of. 1. If the radius of the circle is 9 centimeters, what is the area of sector? 120 Total area of the circle 5 p(9 2 ) 5 81p cm Sector s fraction of the circle 5 120º 1 360º rea of sector 5 (81p) 5 27p 3 The area of sector is 27p cm If the radius of the circle is 16 meters, what is the area of sector D? 45 D 804 hapter Skills Practice

29 Lesson.3 Skills Practice page 3 Name Date 3. If the radius of the circle is 15 feet, what is the area of sector EF? E 30 F 4. If the radius of the circle is inches, what is the area of sector GH? G H 20 hapter Skills Practice 805

30 Lesson.3 Skills Practice page 4 5. If the radius of the circle is 32 centimeters, what is the area of sector IJ? I J If the radius of the circle is 20 millimeters, what is the area of sector KL? 80 L K 806 hapter Skills Practice

31 Lesson.3 Skills Practice page 5 Name Date 7. If the radius of the circle is 24 centimeters, what is the area of sector MN? M 135 N 8. If the radius of the circle is 21 meters, what is the area of sector PQ? P 150 Q hapter Skills Practice 807

32 Lesson.3 Skills Practice page 6 alculate the area of each segment. Round your answer to the nearest tenth, if necessary. Use 3.14 to estimate. 9. If the radius of the circle is 6 centimeters, what is the area of the shaded segment? 90 Total area of the circle 5 p(6 2 ) 5 36p cm Sector s fraction of the circle 5 90º 1 360º rea of sector 5 (36p) 5 9p cm2 4 rea of (6 6) 5 18 cm2 rea of the segment: 9p 2 18 < The area of the shaded segment is approximately.3 cm 2.. If the radius of the circle is 14 inches, what is the area of the shaded segment? D hapter Skills Practice

33 Lesson.3 Skills Practice page 7 Name Date 11. If the radius of the circle is 17 feet, what is the area of the shaded segment? E 90 F 12. If the radius of the circle is 22 centimeters, what is the area of the shaded segment? 90 G H hapter Skills Practice 809

34 Lesson.3 Skills Practice page If the radius of the circle is 25 meters, what is the area of the shaded segment? I J If the radius of the circle is 30 centimeters, what is the area of the shaded segment? 90 K L 8 hapter Skills Practice

35 Lesson.3 Skills Practice page 9 Name Date In circle below, m Use the given information to determine the length of the radius of circle. o 15. If the area of the segment is 16p 2 32 square feet, what is the length of the radius of circle? 16p 5 90º 360º 1 (pr2 ) 16p 5 4 (pr2 ) 64 5 r r The length of the radius is 8 feet. 16. If the area of the segment is 25p 2 50 square inches, what is the length of the radius of circle? 17. If the area of the segment is p 2 2 square meters, what is the length of the radius of circle? hapter Skills Practice 811

36 Lesson.3 Skills Practice page 18. If the area of the segment is 56.25p square yards, what is the length of the radius of circle? 19. If the area of the segment is 121p square feet, what is the length of the radius of circle? 20. If the area of the segment is 90.25p square millimeters, what is the length of the radius of circle? 812 hapter Skills Practice

37 Lesson.4 Skills Practice Name Date ircle K. Excellent! ircle Problems Vocabulary Define the key term in your own words. 1. linear velocity 2. angular velocity hapter Skills Practice 813

38 Lesson.4 Skills Practice page 2 Problem Set Use the given arc measures to determine the measures of the indicated angles X V Y Z D E m ED 5 140º m D 5 º m ED 5 155º m D 5 25º ecause arc D is a semicircle, its measure is 180º. m D 5 m 1 m D 180º 5 m 1 º m 5 170º m ED (m ED 1 m ) m ED 5 1 (140º 1 170º) 2 m ED (3º) m ED 5 155º m D 5 180º 2 155º 5 25º W m XY 5 20º m YZ 5 50º m XVY 5 m YVZ hapter Skills Practice

39 Lesson.4 Skills Practice page 3 Name Date 3. E 4. I J D H L m E 5 20º m D 5 70º m JK 5 164º m I L 5 42º m 5 m H 5 K M D Q N P E m E 5 170º m D 5 20º m MQ 5 50º m NP 5 12º m 5 m 5 hapter Skills Practice 815

40 Lesson.4 Skills Practice page 4 alculate the area of each sector. Use 3.14 for. Round to the nearest hundredth, if necessary D 3 cm F 2 in. E r (3) (9) 5 < 3.14 square centimeters m S R 160. cm 20 T 816 hapter Skills Practice

41 Lesson.4 Skills Practice page 5 Name Date cm 80 D 2 ft 50 E F alculate the area of the shaded segment of the circle in. The area of the shaded segment 5 the area of sector 2 the area of triangle. rea of sector r (3)2 rea of n bh < 1 4 (3.14)(9) < 7.07 square inches (3)(3) square inches 2 rea of segment < < 2.57 square inches hapter Skills Practice 817

42 Lesson.4 Skills Practice page in. M 818 hapter Skills Practice

43 Lesson.4 Skills Practice page 7 Name Date 15. X 2 cm 60 Z Y hapter Skills Practice 819

44 Lesson.4 Skills Practice page Q 6 cm 60 P R Determine each linear or angular velocity. 17. Determine the linear velocity if s 5 12 cm and t 5 2 sec. v 5 s t 5 12 cm 2 sec 5 6 cm/sec 18. Determine the angular velocity if 5 12p and t 5 5p seconds. 820 hapter Skills Practice

45 Lesson.4 Skills Practice page 9 Name Date 19. Determine the linear velocity if s in. and t 5 12 s. 20. Determine the angular velocity if 5 9p and t 5 16 seconds. 21. Determine the linear velocity if s 5 25 ft and t s. 22. Determine the angular velocity if 5 3 p and t 5 p seconds. 4 hapter Skills Practice 821

46 822 hapter Skills Practice

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