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Practice Activities Name Chapter 9, Lessons 11 – 13 List all possible quadrilaterals for each description. 1. exactly one pair of parallel sides 2. four congruent sides trapezoid rhombus, square 3. two pairs of congruent angles 4. two pairs of parallel sides parallelogram, rectangle, rhombus, square parallelogram, rectangle, rhombus, square 5. two pairs of adjacent congruent sides 6. at least three right angles rhombus, square, kite rectangle, square List the missing lengths and angle measures for each figure. 7. rectangle ABCD Copyright © by William H. Sadlier, Inc. Permission to duplicate classroom quantities granted to users of Fundamentals of Algebra. B 1 1 2 in. C 1 in. ____ 3 __ mAB 5 2 1 in. ____ 1 __ mAD 5 2 mABC 5 90° mBCD 5 90° mCDA 5 90° mDBA 5 90° 1 3 2 in. D A 8. parallelogram GHJK ____ 9.3 m H J 3.7 m 8207-W_G7_C09_L11-13_PA01 G 75° K 9. rhombus PQRS P 98° 8207-W_G7_C09_L11-13_PA02 S 17 yd mJK 5 3.7 m mGHJ 5 105° mHJK 5 75° ____ Q R ___ mGK 5 9.3 m ____ mJKG 5 105° ___ mPQ 5 17 yd mQR 5 17 yd mPS 5 17 yd mQPS 5 82° mPSR 5 98° mSRQ 5 82° Tell whether each statement is true or false. Explain your answer. 8207-W_G7_C09_L11-13_PA03 10. All rhombuses are squares. 11. All rectangles are rhombuses. False; All squares are rhombuses, but False; Rhombuses have four congruent not all rhombuses have four right angles. sides, rectangles do not. 12. A rectangle is a parallelogram. 13. A trapezoid can have two right angles. True; As with all parallelograms, a True; A trapezoid can have as many as rectangle has two pairs of parallel sides. two right angles, but the right angles must be adjacent. Course I, Chapter 9 1 (continued) Practice Activities Name Chapter 9, Lessons 11 – 13 Use the circle at the right to answer exercises 14–24. 14. Name the center. A 15. Name 16. Name 17. Name G ____ ___ , EF two diameters. BC ____ ___ ___ ___ ___ ___ , AC , AD , AE , AF , AH six radii. AB ____ ___ ___ ___ , DE , EF , FJ four chords. BC D F B 18. Name two secants. BC, EF C A H 19. Name a tangent. FG E J 20. Name two inscribed angles. DEF, EFJ 21. Name four central angles. Check students’ answers. 22. Name three minor arcs. Check students’ answers. 8207-W_G7_C09_L11-13_PA04 Copyright © by William H. Sadlier, Inc. Permission to duplicate classroom quantities granted to users of Fundamentals of Algebra. 23. Name three major arcs. Check students’ answers. 24. Name four semicircles. BJC, BFC, FDE, FBE. Note: Sample answers given. Use circle Q at the right to answer exercises 25–34. 25. mRS 125° 26. mVR 55° 27. mRVU 136° 28. mVUT 125° 29. mVQR 55° 30. m/VTR 27.5° 31. m/RSV 27.5° 32. m/UQV 81° 33. Name four pairs of supplementary central angles. V R U 44° 125° Q T S Answers may vary, but should include some combination of: /SQT and /TQV; 8207-W_G7_C09_L11-13_PA05 /SQU and /UQV; /VQR and /RQS; /TQU and /UQR. ___ ____ 34. Are SR and TV parallel? Yes. /SQR and /TQV are vertical angles, so SQR and TQV are congruent, using SAS. Since /TRS and /VTR are alternate interior angles, SR and TV must be parallel. Use the figure at the right to answer exercises 35–37. 35. Describe the solid circle in relation to the triangle. The solid circle circumscribes the triangle. 36. Describe the solid circle in relation to the square. The solid circle is inscribed in the square. 37. Describe the dotted circle in relation to the solid circle. The two circles are concentric. Course I, Chapter 9 (continued) Practice Activities Name Chapter 9, Lessons 11 – 13 In order to make a circle graph, find the degrees in the sector for each category. On a separate sheet of paper, make a circle graph for each table. Teachers’ Primary News Sources 38. Source Percent (%) Multiply Degrees in Sector a. Newspaper 15% 0.15 • 360 54° b. Radio 5% 0.05 • 360 18° c. Television 40% 0.40 • 360 144° d. Website 30% 0.30 • 360 108° e. Blog 10% 0.10 • 360 36° Totals 100% 360° Percent of Immigrants by U.S. Region (2005) 39. Source Copyright © by William H. Sadlier, Inc. Permission to duplicate classroom quantities granted to users of Fundamentals of Algebra. Check students’ graphs. Percent (%) Multiply a. Northeast 24% 0.24 • 360 86.4° b. Southeast 17% 0.17 • 360 61.2° c. Midwest 11% 0.11 • 360 39.6° d. Southwest 16% 0.16 • 360 57.6° e. West 32% 0.32 • 360 115.2° Totals 100% Check students’ graphs. Degrees in Sector 360° Solve. Show your work. 40. /ZWX in rhombus WXYZ measures 17°. Name the other angles in the rhombus and tell the measure of each angle. 360 2 (17 1 17) 5 326; 326 4 2 5 163 The other angles are /WXY, /XYZ, and /YZW. Their measures are 163°, 17°, and 163°, respectively. ____ 42. BD is a diameter of circle E. /FED is a central angle and measures 63°. What kind of arc is BDF? What is its measure? 180 1 63 5 243 BDF is a major arc and measures 243°. 41. Cecilia drew a square that measures 6 in. on each side. She then drew a circle inside that square. The circle had a 3 in. radius. What is the relation of the square to the circle? Because the circle’s diameter matches the sides of the square, the square circumscribes the circle. 43. Of a theatre company’s $50,000 budget for a show, $9500 goes to marketing. What would be the measure of the central angle for the marketing sector in a circle graph? 9500 4 50,000 5 19%; 0.19 • 360 5 68.4° The angle for the marketing sector would be 68.4°. Course I, Chapter 9