Riding a Ferris Wheel

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1 Lesson.1 Skills Practice Name ate iding a Ferris Wheel Introduction to ircles Vocabulary Identify an instance of each term in the diagram. 1. center of the circle 6. central angle T H I 2. chord 7. inscribed angle U V N P 3. secant of the circle 8. arc 4. tangent of the circle. major arc 5. point of tangency 10. minor arc 11. diameter 12. semicircle hapter Skills Practice 727

2 Lesson.1 Skills Practice page 2 Problem Set Identify the indicated part of each circle. xplain your answer NP H I N K P Point is the center of the circle. It is a point that is the same distance from each point on the circle F 5. H 6. N H L I K N P 728 hapter Skills Practice

3 Lesson.1 Skills Practice page 3 Name ate 7. SQ 8. TU Q T U S V W Identify each angle as an inscribed angle or a central angle.. U ngle U is an inscribed angle. 10. Z Z K 11. K U 12. ZKU 13. U 14. K hapter Skills Practice 72

4 Lesson.1 Skills Practice page 4 lassify each arc as a major arc, a minor arc, or a semicircle F rc is a minor arc. 17. FHI 18. L F H K I L 1. NPQ 20. TS N P S Q T U raw the part of a circle that is described. 21. raw chord. 22. raw radius. 730 hapter Skills Practice

5 Lesson.1 Skills Practice page 5 Name ate 23. raw secant H. 24. raw a tangent at point. 25. Label the point of tangency. 26. Label center. 27. raw inscribed angle F. 28. raw central angle HI. hapter Skills Practice 731

6 732 hapter Skills Practice

7 Lesson.2 Skills Practice Name ate Take the Wheel entral ngles, Inscribed ngles, and Intercepted rcs Vocabulary efine each term in your own words. 1. degree measure of a minor arc 2. adjacent arcs 3. rc ddition Postulate 4. intercepted arc 5. Inscribed ngle Theorem 6. Parallel Lines ongruent rcs Theorem hapter Skills Practice 733

8 Lesson.2 Skills Practice page 2 Problem Set etermine the measure of each minor arc The measure of is 0º. 3. F 4. H H F 5. I 6. KL 120 I K 85 L 734 hapter Skills Practice

9 Lesson.2 Skills Practice page 3 Name ate etermine the measure of each central angle. 7. m/yz 8. m/t P Y Z T m/yz m/lk 10. m/f 31 K N 72 L 30 8 F 11. m/kws 12. m/viq V 5 W S T K N 22 I Q hapter Skills Practice 735

10 Lesson.2 Skills Practice page 4 etermine the measure of each inscribed angle. 13. m YZ 14. m TU 150 Z T Q U 82 Y m YZ m/kls 16. m V V K L 112 S m Q 18. m SI Q 155 S 28 I 736 hapter Skills Practice

11 Lesson.2 Skills Practice page 5 Name ate etermine the measure of each intercepted arc. 1. m K K 20. m IU L m K L I U 21. m QW 22. m TV Q W T V 23. m m S S 0 P hapter Skills Practice 737

12 Lesson.2 Skills Practice page 6 alculate the measure of each angle. 25. The measure of is 62º. What is the measure of? 1 m 5 (m/) 5 62º 5 31º The measure of is 8º. What is the measure of? 27. The measure of / is 128º. What is the measure of /F? F 738 hapter Skills Practice

13 Lesson.2 Skills Practice page 7 Name ate 28. The measure of /H is 74º. What is the measure of /IH? H I 2. The measure of /K is 168º. What is the measure of /IK? I K 30. The measure of /KL is 148º. What is the measure of /KL? K L hapter Skills Practice 73

14 Lesson.2 Skills Practice page 8 Use the given information to answer each question. 31. In circle, m Z 5 86º. What is m WY? W Z Y m WY In circle, m W 5 102º. What is m YZ? W Y Z 33. In circle, m WZ 5 65º and m Z 5 38º. What is m W? Z W 740 hapter Skills Practice

15 Lesson.2 Skills Practice page Name ate 34. In circle, m W 5 105º. What is m WY? W Y 35. In circle, m WY 5 83º. What is m/z? W Z Y 36. In circle, m WY 5 50º and m YZ 5 30º. What is m WZ? W Z Y hapter Skills Practice 741

16 742 hapter Skills Practice

17 Lesson.3 Skills Practice Name ate anhole overs easuring ngles Inside and utside of ircles Vocabulary efine each theorem in your own words. 1. Interior ngles of a ircle Theorem 2. xterior ngles of a ircle Theorem 3. Tangent to a ircle Theorem Problem Set Write an expression for the measure of the given angle. 1. m P 2. m P N Q m P ( m 1 m QN ) hapter Skills Practice 743

18 Lesson.3 Skills Practice page 2 3. m NK 4. m UWV L N K U V W Y 5. m SWT 6. m HI S W T F V U H I List the intercepted arc(s) for the given angle. 7. Q 8. SU Q S T N P U P NP, Q 744 hapter Skills Practice

19 Lesson.3 Skills Practice page 3 Name ate. FH 10. ZW F I Y W H Z L Z Z K L Write an expression for the measure of the given angle. 13. m 14. m UY W Y m ( m 2 m ) U Z hapter Skills Practice 745

20 Lesson.3 Skills Practice page m ST 16. m F U F S V T H I 17. m 18. m LPN F H L N p Q 746 hapter Skills Practice

21 Lesson.3 Skills Practice page 5 Name ate reate a proof to prove each statement. 1. iven: hords and intersect at point. Prove: m ( m 1 m ) Statements easons 1. hords and intersect at 1. iven point. 2. raw chord 2. onstruction 3. m 1 5 m 1 m 3. xterior ngle Theorem 4. m 5 2 m 4. Inscribed ngle Theorem 1 5. m 5 2 m m 5 2 m 1 2 m 7. m ( m 1 m ) 5. Inscribed ngle Theorem 6. Substitution 7. istributive Property hapter Skills Practice 747

22 Lesson.3 Skills Practice page iven: Secant QT and tangent S intersect at point S. Prove: m QS 5 1 ( 2 m Q 2 m T ) Q P T S 748 hapter Skills Practice

23 Lesson.3 Skills Practice page 7 Name ate 21. iven: Tangents VY and Y intersect at point Y. Prove: m Y ( m VW 2 m V ) V Y W hapter Skills Practice 74

24 Lesson.3 Skills Practice page iven: hords FI and H intersect at point. Prove: m FH ( m FH 1 m I ) F H I 750 hapter Skills Practice

25 Lesson.3 Skills Practice page Name ate 23. iven: Secant L and tangent NL intersect at point L. Prove: m L ( m 2 m K ) K L N hapter Skills Practice 751

26 Lesson.3 Skills Practice page iven: Tangents S and U intersect at point. Prove: m ( m VTW 2 m VW ) T S U V W 752 hapter Skills Practice

27 Lesson.3 Skills Practice page 11 Name ate Use the diagram shown to determine the measure of each angle or arc. 25. etermine m FI. m/k 5 20 m 5 80 F K 26. etermine m KL. m K m N K I The measure 1 of arc FI is 120 degrees. m/k 5 2 (m FI 5 m ) (m FI 2 80) 40 5 m FI 2 80 m FI L N hapter Skills Practice 753

28 Lesson.3 Skills Practice page etermine m. m VW 5 50 m TU etermine m WY. m WUY W T U S U V W Y Z 754 hapter Skills Practice

29 Lesson.3 Skills Practice page 13 Name ate 2. etermine m S. m UV 5 30 m/ts 5 80 S 30. etermine m. m Z m 5 30 Z T U V hapter Skills Practice 755

30 756 hapter Skills Practice

31 Lesson.4 Skills Practice Name ate olor Theory hords Vocabulary atch each definition with its corresponding term. 1. iameter hord Theorem a. If two chords of the same circle or congruent circles are congruent, then their corresponding arcs are congruent. 2. quidistant hord Theorem b. The segments formed on a chord when two chords of a circle intersect 3. quidistant hord c. If two chords of the same circle or congruent onverse Theorem circles are congruent, then they are equidistant from the center of the circle. 4. ongruent hord ongruent d. If two arcs of the same circle or congruent rc Theorem circles are congruent, then their corresponding chords are congruent. 5. ongruent hord ongruent rc e. If two chords of the same circle or congruent onverse Theorem circles are equidistant from the center of the circle, then the chords are congruent. 6. segments of a chord f. If two chords of a circle intersect, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments in the second chord. 7. Segment hord Theorem g. If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and bisects the arc determined by the chord. hapter Skills Practice 757

32 Lesson.4 Skills Practice page 2 Problem Set Use the given information to answer each question. xplain your answer. 1. If diameter bisects, what is the angle of intersection? The angle of intersection is 0º because diameters that bisect chords are perpendicular bisectors. 2. If diameter FH intersects at a right angle, how does the length of I compare to the length of I? F I H 3. How does the measure of KL and L compare? L N K 758 hapter Skills Practice

33 Lesson.4 Skills Practice page 3 Name ate 4. If KP > LN, how does the length of Q compare to the length of? K L Q P N 5. If Y > Z, what is the relationship between TU and V? S U Y T V Z W 6. If > H and diameter is perpendicular to both, what is the relationship between F and HK? I H F K hapter Skills Practice 75

34 Lesson.4 Skills Practice page 4 etermine each measurement. 7. If is a diameter, what is the length of? 5 cm cm 8. If the length of is 13 millimeters, what is the length of?. If the length of is 24 centimeters, what is the length of? 10. If the length of F is 32 inches, what is the length of H? F H 760 hapter Skills Practice

35 Lesson.4 Skills Practice page 5 Name ate 11. If the measure of 5 155º, what is the measure of? 12. If segment is a diameter, what is the measure of? ompare each measurement. xplain your answer. 13. If > F, how does the measure of and F compare? F The measure of is equal to the measure of F because the corresponding arcs of congruent chords are congruent. hapter Skills Practice 761

36 Lesson.4 Skills Practice page If K > L, how does the measure of L and K compare? K L 15. If Q > PS, how does the measure of QP and PS compare? Q P S 16. If > H, how does the measure of and H compare? F H 762 hapter Skills Practice

37 Lesson.4 Skills Practice page 7 Name ate 17. If >, what is the relationship between and? 18. If H > F, what is the relationship between H and F? H F Use each diagram and the Segment hord Theorem to write an equation involving the segments of the chords. 1. F 20. L Q P N H? 5 F? H hapter Skills Practice 763

38 Lesson.4 Skills Practice page T V 22. S K H V 23. I 24. Y U L V 764 hapter Skills Practice

39 Lesson.5 Skills Practice Name ate Solar clipses Tangents and Secants Vocabulary Write the term from the box that best completes each statement. external secant segment Secant Segment Theorem tangent segment secant segment Secant Tangent Theorem Tangent Segment Theorem 1. (n) is the segment that is formed from an exterior point of a circle to the point of tangency. 2. The states that if two tangent segments are drawn from the same point on the exterior of the circle, then the tangent segments are congruent. 3. When two secants intersect in the exterior of a circle, the segment that begins at the point of intersection, continues through the circle, and ends on the other side of the circle is called a(n). 4. When two secants intersect in the exterior of a circle, the segment that begins at the point of intersection and ends where the secant enters the circle is called a(n). 5. The states that if two secants intersect in the exterior of a circle, then the product of the lengths of the secant segment and its external secant segment is equal to the product of the lengths of the second secant segment and its external secant segment. 6. The states that if a tangent and a secant intersect in the exterior of a circle, then the product of the lengths of the secant segment and its external secant segment is equal to the square of the length of the tangent segment. hapter Skills Practice 765

40 Lesson.5 Skills Practice page 2 Problem Set alculate the measure of each angle. xplain your reasoning. 1. If is a radius, what is the measure of /? The measure of angle is 0 degrees because a tangent line and the radius that ends at the point of tangency are perpendicular. 2. If is a radius, what is the measure of /? 3. If Y is a radius, what is the measure of / Y? Y 766 hapter Skills Practice

41 Lesson.5 Skills Practice page 3 Name ate 4. If S is a tangent segment and S is a radius, what is the measure of /S? 35 S 5. If UT is a tangent segment and U is a radius, what is the measure of /TU? 23 T U hapter Skills Practice 767

42 Lesson.5 Skills Practice page 4 6. If V W is a tangent segment and V is a radius, what is the measure of /VW? V 72 W Write a statement to show the congruent segments. 7. and are tangent to circle. 8. Z and ZW are tangent to circle. Z W >. S and T are tangent to circle. 10. P and NP are tangent to circle. S N T P 768 hapter Skills Practice

43 Lesson.5 Skills Practice page 5 Name ate 11. and F are tangent to circle. 12. H and I are tangent to circle. H F I alculate the measure of each angle. xplain your reasoning. 13. If F and F are tangent segments, what is the measure of /F? F 64 The measure of angle F is 58 degrees. I know triangle F is isosceles and its base angles are congruent. Let x represent the measure of angle F and the measure of angle F. m/f 1 x 1 x x x x 5 58 hapter Skills Practice 76

44 Lesson.5 Skills Practice page If HI and I are tangent segments, what is the measure of /HI? H 48 I 15. If K and L are tangent segments, what is the measure of /KL? K L hapter Skills Practice

45 Lesson.5 Skills Practice page 7 Name ate 16. If NP and QP are tangent segments, what is the measure of /NPQ? P N 71 Q 17. If F and VF are tangent segments, what is the measure of / VF? V 22 F hapter Skills Practice 771

46 Lesson.5 Skills Practice page If T and T are tangent segments, what is the measure of /T? 33 T Name two secant segments and two external secant segments for circle. 1. P Q 20. T S Secant segments: PT and QT xternal secant segments: T and ST 21. U V W 22. L N P Y 772 hapter Skills Practice

47 Lesson.5 Skills Practice page Name ate 23. F 24. H N I K L Use each diagram and the Secant Segment Theorem to write an equation involving the secant segments. 25. S T U V 26. N Q S V? TV 5 SV? UV I H K L hapter Skills Practice 773

48 Lesson.5 Skills Practice page V F W Y Z Name a tangent segment, a secant segment, and an external secant segment for circle. 31. S T 32. I U H K Tangent segment: TU Secant segment: T xternal secant segment: ST 33. F 34. P Q S 774 hapter Skills Practice

49 Lesson.5 Skills Practice page 11 Name ate 35. H 36. W y F Z Use each diagram and the Secant Tangent Theorem to write an equation involving the secant and tangent segments Q W S V ( ) 2 5 Q? W 3. Z 40. T I hapter Skills Practice 775

50 Lesson.5 Skills Practice page U 42. V Q l W 776 hapter Skills Practice

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