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4. Transformations Tessellations and Fractals Geometric Properties Special Right Triangles Transformations on a Grid 100 200 300 400 500 Final Jeopardy Jeopardy Board

5. BoardAnswer 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°

6. Board 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°

7. BoardAnswer 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°

8. Board 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° 47° 79° _____?

9. BoardAnswer 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

10. Board Transformations Tessellations and Fractals 300 F 243 G 54 H 81 J 27 13927 5 th Stage? _____ 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?

11. F G H J BoardAnswer 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?

12. Board Transformations Tessellations and Fractals 400 F G H J 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?

13. BoardAnswer 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

14. Board 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 45° ccw Try: A T to U

15. A 30(n + 1) B C 30(n − 1) D BoardAnswer 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?

16. Board Geometric Properties 100 A 30(n + 1) B C 30(n − 1) D 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? # SidesDegrees 3 120 4 90 6 60 ( ) ✘ ✘

17. BoardAnswer 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? 1 st Ave 2 nd Ave

18. 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 Geometric Properties 200 1 st Ave 2 nd Ave F 90°, 65°, 25° G90°, 50°, 40° H 90°, 60°, 30° J 130°, 40°, 10° 40° 90°50° Straight angle = ______180° 50°

19. BoardAnswer 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 2 n H 2n − 1 J2 n − 1

20. Board 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 2 n H 2n − 1 J2 n − 1 StageCircles 11 23 37

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

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

23. BoardAnswer 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.

24. 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 Geometric Properties 500 130° There are 3 triangle in the figure 3(180°) = 540° 90° 140° 1 4 0

25. BoardAnswer 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.

26. Board Special Right Triangles 100 F 12 ft G17 ft H 21 ft J 24 ft Length of each side = ______ 12 ft The length of the diagonal is _____ ft 12 ft a 2 + b 2 = c 2 12 2 + 12 2 = c 2 144 + 144 = c 2 288 = c 2 16.97 = c

27. BoardAnswer 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?

28. Board 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? F 110 ft G 127 ft H156 ft J 311 ft 220 ft The height of the kite is _____ ft a 2 + b 2 = c 2 a 2 + b 2 = 220 2 a 2 + a 2 = 220 2 2a 2 = 48400 22 a 2 = 24200

29. BoardAnswer Special Right Triangles 300 A 20 mm B 20 mm C 60 mm D40 mm ∆WXY is a right triangle. Find the length of

30. A 20 mm B 20 mm C 60 mm D40 mm Board Special Right Triangles 300 ∆WXY is a right triangle. Find the length of m  Y = ____ 30° 60° 80 mm

31. Board Special Right Triangles 300 ∆WXY is a right triangle. Find the length of A 20 mm B 20 mm C 60 mm D40 mm m  Y = ____ 30° 60° 80 mm a 2 + b 2 = c 2 40 2 + b 2 = 80 2 1600 + b 2 = 6400 -1600 b 2 = 4800 b = 69.282

32. BoardAnswer 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?

33. F 1.7 ft G 18 ft H 10.4 ft J6 ft Board 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? 60° 12 ft 6 ft 12 ft

34. F 1.7 ft G 18 ft H 10.4 ft J6 ft Board 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? 60° 12 ft 6 ft 12 ft

35. BoardAnswer 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?

36. Board Special Right Triangles 500 A 13.4 in. B10.4 in. C 8.5 in. D 5.2 in. 12 ft 6 ft a 2 + b 2 = c 2 6 2 + b 2 = 12 2 36 + b 2 = 144 -36 b 2 = 108 b = 10.392

37. BoardAnswer Transformations on a Grid 100 Find the coordinates of the vertices of the rectangle if it is translated 3 units right and 3 units down

38. Board Transformations on a Grid 100 Find the coordinates of the vertices of the rectangle if it is translated 3 units right and 3 units down (3,0)(9,0) (9,2) (3,2)

39. BoardAnswer Transformations on a Grid 200 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

40. Board Transformations on a Grid 200 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

41. BoardAnswer Transformations on a Grid 300 Which pair of the following polygons is congruent? F Polygon A and C G Polygon B and D H Polygon A and B JPolygon B and C

42. Board Transformations on a Grid 300 Which pair of the following polygons is congruent? F Polygon A and C G Polygon B and D H Polygon A and B JPolygon B and C 3 2.5 3 4

43. BoardAnswer Transformations on a Grid 400 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 DTranslate figure MNPQ to the left 6 and down 5

44. 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 DTranslate figure MNPQ to the left 6 and down 5 Board Transformations on a Grid 400 (6, 5)

45. BoardAnswer Transformations on a Grid 500 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)

46. Board Transformations on a Grid 500 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)

47. Final Jeopardy Category Board

48. Final Jeopardy Question Answer 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.

49. Board Final Jeopardy Answer In the figure below, what is the length of ML in centimeters? 35 cm 28 cm a 2 + b 2 = c 2 28 2 + b 2 = 35 2 784 + b 2 = 1225 -784 b 2 = 441 b = 21 28 cm 100 cm 21 cm a 2 + b 2 = c 2 28 2 + b 2 = 100 2 784 + b 2 = 10000 -784 b 2 = 9216 b = 9696 cm ML = 21 + 96 = 117 cm 1 1 7