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Let’s Get Ready

Let’s Get Ready. To Play Some. J. E. O. P. A. R. D. Y. J E O P A R D Y. J E O P A R D Y. J E O P A R D Y. J E O P A R D Y. J E O P A R D Y. Jeopardy Board. Final Jeopardy. Transformations Tessellations and Fractals 100.

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Let’s Get Ready

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  1. Let’s Get Ready To Play Some . . .

  2. J E O P A R D Y JEOPARDY JEOPARDY JEOPARDY JEOPARDY JEOPARDY

  3. Jeopardy Board Final Jeopardy

  4. Transformations Tessellations and Fractals 100 The figure below shows the positions of a surveying crew measuring the distance to a tree across the river. Which of the following best represents the measure of TAP? A 58° B 69° C 90° D 122° Board Answer

  5. Transformations Tessellations and Fractals 100 The figure below shows the positions of a surveying crew measuring the distance to a tree across the river. Which of the following best represents the measure of TAP? A 58° B 69° C 90° D 122° Board

  6. Transformations Tessellations and Fractals 200 The figure below shows Aaron’s recent hiking course, which started at point L, went to point M and then point P, and then returned to point L. What is the measure of LMP formed by Aaron’s hiking course? A 101° B 79° C 54° D 43° Board Answer

  7. Transformations Tessellations and Fractals 200 The figure below shows Aaron’s recent hiking course, which started at point L, went to point M and then point P, and then returned to point L. What is the measure of LMP formed by Aaron’s hiking course? 79° A 101° B 79° C 54° D 43° _____? 47° Board

  8. Transformations Tessellations and Fractals 300 The first 4 stages of a certain fractal are shown below. In each stage after the first, each square is divided into 4 squares, and then the bottom right square is removed. If the pattern continues, how many shaded square units will Stage 5 contain? F 243 G 54 H 81 J 27 Board Answer

  9. Transformations Tessellations and Fractals 300 The first 4 stages of a certain fractal are shown below. In each stage after the first, each square is divided into 4 squares, and then the bottom right square is removed. If the pattern continues, how many shaded square units will Stage 5 contain? F 243 G 54 H 81 J 27 1 3 9 27 Board 5th Stage? _____

  10. Transformations Tessellations and Fractals 400 Start with a 1-unit-by-1-unit unshaded square. In each iteration, the following steps occur for the smallest unshaded squares resulting from the previous iteration. Step 1: Divide the square into a 3-by-3 grid of squares Step 2: Shade only the center square of this 3-by-3 grid What fraction of the 1-unit-by-1-unit square is shaded after the second iteration? F G H J Board Answer

  11. Transformations Tessellations and Fractals 400 Start with a 1-unit-by-1-unit unshaded square. In each iteration, the following steps occur for the smallest unshaded squares resulting from the previous iteration. Step 1: Divide the square into a 3-by-3 grid of squares Step 2: Shade only the center square of this 3-by-3 grid What fraction of the 1-unit-by-1-unit square is shaded after the second iteration? F G H J Board

  12. Transformations Tessellations and Fractals 500 The regular octagon below shows selected positions on a combination lock. The dial of the lock is turned 90° clockwise and then 45° counterclockwise. Which pair of points can describe the starting and ending points of a marker on the dial of this lock? A T to U B S to V C W to V D Z to W Board Answer

  13. Transformations Tessellations and Fractals 500 The regular octagon below shows selected positions on a combination lock. The dial of the lock is turned 90° clockwise and then 45° counterclockwise. Which pair of points can describe the starting and ending points of a marker on the dial of this lock? A T to U B S to V C W to V D Z to W 90° clockwise Try: A T to U 45° ccw Board

  14. Geometric Properties 100 The measure of an exterior angle is shown for each of 3 regular polygons below. Which expression best represents the measure in degrees of an exterior angle of a regular polygon with n sides? A 30(n + 1) B C 30(n − 1) D Board Answer

  15. Geometric Properties 100 The measure of an exterior angle is shown for each of 3 regular polygons below. Which expression best represents the measure in degrees of an exterior angle of a regular polygon with n sides? A 30(n + 1) B C 30(n − 1) D ✘ ( ) ✘ ( ) # Sides Degrees 3 120 4 90 Board 6 60

  16. 1st Ave 2nd Ave Geometric Properties 200 On the map below, First Avenue and Second Avenue are parallel. A city planner proposes to locate a small garden and park on the triangular island formed by the intersections of four streets shown below. What are the measures of the three angles of the garden? Board Answer

  17. 1st Ave 2nd Ave Geometric Properties 200 On the map below, First Avenue and Second Avenue are parallel. A city planner proposes to locate a small garden and park on the triangular island formed by the intersections of four streets shown below. What are the measures of the three angles of the garden? 50° 90° F 90°, 65°, 25° G 90°, 50°, 40° H 90°, 60°, 30° J 130°, 40°, 10° 40° Straight angle = ______ 180° Board 50°

  18. Geometric Properties 300 The figure below shows the first 3 stages of a fractal. How many circles will the nth stage of this fractal contain? F 2n G 2n H 2n − 1 J 2n− 1 Board Answer

  19. Geometric Properties 300 The figure below shows the first 3 stages of a fractal. How many circles will the nth stage of this fractal contain? F 2n G 2n H 2n − 1 J 2n− 1 1 1 2 3 Board 3 7

  20. A n − 3 B C D n(n − 3) Geometric Properties 400 Use the table to determine the expression that best represents the number of diagonals of any convex polygon having n sides. Board Answer

  21. A n − 3 B C D n(n − 3) Geometric Properties 400 Use the table to determine the expression that best represents the number of diagonals of any convex polygon having n sides. Board

  22. Geometric Properties 500 In the figure shown below, BC is parallel to ED, and AE is perpendicular to ED. The measure of ∠ABC is 130°. What is the measure of ∠BAE in degrees? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. Board Answer

  23. Geometric Properties 500 In the figure shown below, BC is parallel to ED, and AE is perpendicular to ED. The measure of ∠ABC is 130°. What is the measure of ∠BAE in degrees? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. 130° There are 3 triangle in the figure 1 4 0 90° 140° 3(180°) = 540° Board 90° 90°

  24. Special Right Triangles 100 A fence around a square garden has a perimeter of 48 feet. Find the approximate length of the diagonal of this square garden. Board Answer

  25. Special Right Triangles 100 A fence around a square garden has a perimeter of 48 feet. Find the approximate length of the diagonal of this square garden. The length of the diagonal is _____ ft F 12 ft G 17 ft H 21 ft J 24 ft a2 + b2 = c2 122 + 122 = c2 144 + 144 = c2 12 ft 12 ft 12 ft Length of each side = ______ 288 = c2 Board 16.97 = c

  26. Special Right Triangles 200 A kite string is 220 feet long from the kite to the ground. The string makes a 45° angle with the ground. About how high off the ground is the kite? Board Answer

  27. Special Right Triangles 200 A kite string is 220 feet long from the kite to the ground. The string makes a 45° angle with the ground. About how high off the ground is the kite? 220 ft F 110 ft G 127 ft H 156 ft J 311 ft a2 + b2 = c2 a2 + b2 = 2202 a2 + a2 = 2202 2a2 = 48400 2 2 a2 = 24200 The height of the kite is _____ ft Board

  28. Special Right Triangles 300 ∆WXY is a right triangle. Find the length of A 20 mm B 20mm C 60 mm D 40 mm Board Answer

  29. Special Right Triangles 300 ∆WXY is a right triangle. Find the length of A 20 mm B 20mm C 60 mm D 40 mm 60° 80 mm 80 mm 30° m Y = ____ 30° 80 mm Board

  30. Special Right Triangles 300 ∆WXY is a right triangle. Find the length of A 20 mm B 20mm C 60 mm D 40 mm 60° 80 mm 80 mm a2 + b2 = c2 402 + b2 = 802 1600 + b2 = 6400 30° -1600 -1600 m Y = ____ 30° b2 = 4800 b = 69.282 80 mm Board

  31. Special Right Triangles 400 The 12-foot-long bed of a dump truck loaded with debris must rise to an angle of 30° before the debris will spill out. Approximately how high must the front of the bed rise for the debris to spill out? Board Answer

  32. Special Right Triangles 400 The 12-foot-long bed of a dump truck loaded with debris must rise to an angle of 30° before the debris will spill out. Approximately how high must the front of the bed rise for the debris to spill out? F 1.7 ft G 18 ft H 10.4 ft J 6 ft 60° 6 ft 12 ft 12 ft 60° Board

  33. Special Right Triangles 400 The 12-foot-long bed of a dump truck loaded with debris must rise to an angle of 30° before the debris will spill out. Approximately how high must the front of the bed rise for the debris to spill out? F 1.7 ft G 18 ft H 10.4 ft J 6 ft 60° 6 ft 12 ft 12 ft 60° Board

  34. Special Right Triangles 500 Megan is using an equilateral triangle as part of a design on a sweatshirt. Each side of the triangle is 12 inches long. Megan is sewing a line of sequins from the midpoint of one side of this triangle to the opposite vertex. Approximately how long will the line of sequins be? Board Answer

  35. Special Right Triangles 500 Megan is using an equilateral triangle as part of a design on a sweatshirt. Each side of the triangle is 12 inches long. Megan is sewing a line of sequins from the midpoint of one side of this triangle to the opposite vertex. Approximately how long will the line of sequins be? A 13.4 in. B 10.4 in. C 8.5 in. D 5.2 in. 12 ft 12 ft a2 + b2 = c2 6 ft 62 + b2 = 122 36 + b2 = 144 12 ft -36 -36 b2 = 108 Board b = 10.392

  36. Transformations on a Grid100 Find the coordinates of the vertices of the rectangle if it is translated 3 units right and 3 units down Board Answer

  37. Transformations on a Grid100 Find the coordinates of the vertices of the rectangle if it is translated 3 units right and 3 units down (9,2) (3,2) (3,0) (9,0) Board

  38. Transformations on a Grid200 Look at the triangles graphed on the grid below. Which of the following correctly describes two triangles, one a single reflection of the other across the x-axis? A KLM  PNM B KRM  PQM C KRM  PNM D KLM  KRM Board Answer

  39. Transformations on a Grid200 Look at the triangles graphed on the grid below. Which of the following correctly describes two triangles, one a single reflection of the other across the x-axis? A KLM  PNM B KRM  PQM C KRM  PNM D KLM  KRM Board

  40. Transformations on a Grid300 Which pair of the following polygons is congruent? F Polygon A and C G Polygon B and D H Polygon A and B J Polygon B and C Board Answer

  41. Transformations on a Grid300 Which pair of the following polygons is congruent? F Polygon A and C G Polygon B and D H Polygon A and B J Polygon B and C 2.5 3 4 3 Board

  42. Transformations on a Grid400 Figure MNPQ is shown on the coordinate plane. Which transformation creates an image with a vertex at the origin? A Rotate figure MNPQ 90° around M B Reflect figure MNPQ across the line x = 1 C Reflect figure MNPQ across the line y = 2.5 D Translate figure MNPQ to the left 6 and down 5 Board Answer

  43. Transformations on a Grid400 Figure MNPQ is shown on the coordinate plane. Which transformation creates an image with a vertex at the origin? A Rotate figure MNPQ 90° around M B Reflect figure MNPQ across the line x = 1 C Reflect figure MNPQ across the line y = 2.5 D Translate figure MNPQ to the left 6 and down 5 (6, 5) Board

  44. Transformations on a Grid500 Which coordinates are the vertices of a triangle congruent to ∆MNP? F (−11, 13), (−9, 16), (−4, 16) G (−8, 5), (−5, 2), (−1, 4) H (−20, 4), (−17, 7), (−12, 5) J (−15, 14), (−18, 17), (−17, 22) Board Answer

  45. Transformations on a Grid500 Which coordinates are the vertices of a triangle congruent to ∆MNP? F (−11, 13), (−9, 16), (−4, 16) G (−8, 5), (−5, 2), (−1, 4) H (−20, 4), (−17, 7), (−12, 5) J (−15, 14), (−18, 17), (−17, 22) Board

  46. Final Jeopardy Category Special Right Triangles Board

  47. Final Jeopardy Question In the figure below, what is the length of ML in centimeters? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. Answer

  48. Final Jeopardy Answer In the figure below, what is the length of ML in centimeters? ML = 21 + 96 = 117 cm 35 cm 28 cm a2 + b2 = c2 282 + b2 = 352 a2 + b2 = c2 784 + b2 = 1225 282 + b2 = 1002 -784 -784 784 + b2 = 10000 b2 = 441 1 1 7 -784 -784 b = 21 21 cm b2 = 9216 b = 96 96 cm 28 cm 100 cm Board

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