1. Geometry Trigonometry
Do Bees Build It Best?
Geometry
Trigonometry

2. BUILDING THE BEST

3. NAILING DOWN AREA

4. HOW MANY CAN YOU FIND?

5. THAT’S ALL THERE IS!

6. HALVING YOUR WAY

7. PARALLELOGRAMS AND TRAPEZOIDS

8. FORMING FORMULAS

9. GOING INTO THE GALLERY

10. A RIGHT-TRIANGLE PAINTING

11. A TRIGONOMETRIC SUMMARY

12. MORE GALLERY MEASUREMENTS

13. A HOMEMADE TRIG TABLE

14. SHADOWS AND SAILBOATS

15. TRI-SQUARE RUG GAMES

16. ANY TWO SIDES WORK
LEG^2 + LEG^2 = HYP^2

17. IMPOSSIBLE RUGS

18. MAKE THE LINES COUNT

19. PROOF BY RUGS

20. THE POWER OF PYTHAGORAS

21. LESLIE’S FERTILE FLOWERS

22. FLOWERS FROM DIFFERENT SIDES

23. DON’T FENCE ME IN

24. RECTANGLES ARE BORING!

25. MORE FENCING, BIGGER CORRALS

26. MORE OPINIONS ABOUT CORRALS

27. BUILDING THE BEST FENCE

28. FALLING BRIDGES

29. LESLIE’S FLORAL ANGLES

30. FLAT CUBES

31. FLAT BOXES

32. A VOLUMINOUS TASK

33. PUT YOUR FIST INTO IT

34. THE INS AND OUTS OF BOXES

35. A SCULPTURE GARDEN

36. THE WORLD OF PRISMS

37. SHEDDING LIGHT ON PRISMS

38. PYTHAGORAS AND THE BOX

39. BACK ON THE FARM

40. WHICH HOLDS MORE?

41. CEREAL BOX SIZES

42. A-TESSELLATING WE GO

43. A PORTFOLIO OF FORMULAS

44. THAT’S ALL THERE IS! EACH TRIANGLE MUST HAVE AN AREA OF 2 UNITS
EACH TRIANGLE MUST HAVE ITS VERTICES ON PEGS
EACH TRIANGLE MUST HAVE A HORIZONTAL SIDE

45. HALVING YOUR WAY

46. FORMING FORMULAS
LOOK FOR WAYS TO CUT UP THE PARALLELOGRAMS AND TRAPEZOIDS INTO TRIANGLES

47. GOING INTO THE GALLERY
REMEMBER, THE HEIGHT IS ALSO THE ALTITUDE WHICH IS DRAWN PERPENDICULAR TO THE BASE

48. A RIGHT-TRIANGLE PAINTING
DRAW A RIGHT TRIANGLE THAT HAS A 55 DEGREE ANGLE
EXTEND BOTH SIDES SO THAT THEY ARE AT LEAST 10 CM IN LENGTH

49. A TRIGONOMETRIC SUMMARY
SIN A = OPPOSITE/HYPOTENUSE
COS A = ADJACENT/HYPOTENUSE
TAN A =
OPPOSITE/ADJACENT

50. A HOMEMADE TRIG TABLE
DRAW A RIGHT TRIANGLE USING THE ASSIGNED ANGLE FOR YOUR GROUP
MEASURE ALL THE SIDES
COMPUTE THE RATIOS OF SIN, COS, AND TAN

51. MORE GALLERY MESUREMENTS
SIN A = OPPOSITE/HYPOTENUSE
COS A = ADJACENT/HYPOTENUSE
TAN A =
OPPOSITE/ADJACENT

52. SHADOWS AND SAILBOATS

53. TRI-SQUARE RUG GAMES
AL WINS WHEN THE LARGEST OF THE 3 SQUARES HAS THE MOST AREA.
WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

54. TRI-SQUARE RUG GAMES
BETTY WINS IF THE TWO SMALLER SQUARES HAVE MORE AREA THEN THE LARGEST
WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

55. TRI-SQUARE RUG GAMES
IF THE TWO SMALLER SQUARES HAVE THE SAME AREA AS THE LARGEST, THIS IS A FAIR GAME.
WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

56. ANY TWO SIDES WORK

57. ANY TWO SIDES WORK

58. ANY TWO SIDES WORK

59. IMPOSSIBLE RUGS
RULE: ANY TWO SIDES OF A TRIANGLE MUST BE GREATER THAN THE THIRD SIDE

60. MAKE THE LINES COUNT

61. THE POWER OF PYTHAGORAS

62. THE POWER OF PYTHAGORAS

63. LESLIE’S FERTILE FLOWERS

64. FLOWERS FROM DIFFERENT SIDES

65. DON’T FENCE ME IN RANCHER GONZALES CAN ONLY AFFORD 300 FEET OF FECNING
MAKE AN INOUT TABLE OF VARIOUS LENGTHS AND WIDTHS

66. RECTANGLES ARE BORING!
RANCHER GONZALE’S NEPHEW JUAN HAS SUGGESTED RECTANGLES
AGAIN SHE MUST USE 300 FEET OF FENCING

67. MORE FENCING, BIGGER CORRALS
HOW DOES THE AREA OF A SQUARE CORRAL MADE 300 FT OF FENCING COMPARE TO 600 FT?

68. MORE FENCING, BIGGER CORRALS
HOW DOES THE AREA OF A AN EQUILATERAL TRIANGLE CORRAL MADE 300 FT OF FENCING COMPARE TO 600 FT?

69. MORE OPINIONS ABOUT CORRALS
ACES : PENTAGON
TWO’S: HEXAGON
THREE’S: SEPTAGON
FOUR’S: OCTAGON
FIVE’S: 9 SIDED REG-POLY
SIXE’S: 10 SIDED REG-POLY

70. BUILDING THE BEST FENCE
AREA=
(P^2/4n) * tan (90-180/n)

71. FALLING BRIDGES
USE OTHER APPROXIMATIONS FOR THE SQUARE ROOT OF 2

72. LESLIE’S FLORAL ANGLES
REMEMBER, THE INVERSE OF:
ADDING?
MULTIPLYING?
SOMETHING SQUARED?
NOW WE NEED THE INVERSE OF OUR TRIG FUNCTIONS

73. FLAT BOXES
132 CM SQUARED

74. FLAT BOXES
108 CM SQUARED

75. A VOLUMINOUS TASK
SURFACE AREA VOLUME #1 #2 #3 #4 #5

76. A VOLUMINOUS TASK
SURFACE AREA VOLUME #7 #8 #9
#10

77. PUT YOUR FIST INTO IT

78. THE INS AND OUTS OF BOXES

79. A SCULPTURE GARDEN
FIND A WAY TO ARRANGE 8 CUBES THAT USES THE LEAST AMOUNT OF PAINT

80. THE WORLD OF PRISMS PRISM IS A SPECIAL TYPE OF SOLID GEOMETRIC FIGURE
THE INTIAL AND FINAL FACES ARE THE BASES
USUALLY 1 OR 2 BASES
PERPENDICULAR DISTANCE BETWEEN THE BASES IS THE HEIGHT

81. THE WORLD OF PRISMS TRIANGULAR PRISMS HEXAGONAL PRISMS
RECTANGULAR PRISMS

82. THE WORLD OF PRISMS
RIGHT PRISMS
OBLIQUE PRISMS

83. THE WORLD OF PRISMS LATERAL FACES LATERAL EDGES BASES
LATERAL SURFACE AREA
TOTAL SURFACE AREA

84. PYTHAGORAS AND THE BOX

85. BACK ON THE FARM