Euclidean and Non-Euclidean Geometry

2. Euclidean and Non-Euclidean Geometry

3. Perspective

4. The Golden Ratio

5. Polygons and Stars

6. Tesselations and Fractals

7. Right Triangles

8. Euclidean and Non-Euclidean Geometry The Golden Ratio Polygons and Stars Tesselations and Fractals Right Triangles Perspective $100 $100 $100 $100 $100 $100 $200 $200 $200 $200 $200 $200 $300 $300 $300 $300 $300 $300 $400 $400 $400 $400 $400 $400 $500 $500 $500 $500 $500 $500

9. Euclidean and Non-Euclidean Geometry $100 Tell whether the angle is acute, right, obtuse or straight.

10. Euclidean and Non-Euclidean Geometry $100 Straight Angle

11. Euclidean and Non-Euclidean Geometry $200 Tell whether the angle is acute, right, obtuse or straight.

12. Euclidean and Non-Euclidean Geometry $200 obtuse

13. Euclidean and Non-Euclidean Geometry $300 Determine whether the polygon is concave or convex.

14. Euclidean and Non-Euclidean Geometry Concave

15. Euclidean and Non-Euclidean Geometry What is the measure of angle Z in the triangle below?

16. Euclidean and Non-Euclidean Geometry 71o

17. Euclidean and Non-Euclidean Geometry An isosceles triangle has an angle with a measure of 34o. What is the largest possible measure of the remaining angles?

18. Euclidean and Non-Euclidean Geometry 112o

19. Perspective Determine whether one-point or two-point perspective is used in the drawing.

21. Perspective One-point Perspective

22. Perspective Describe the type of perspective used in the drawing on the next screen: Atmospheric, overlapping images, or diminishing sizes?

24. Perspective Overlapping Images

25. Perspective Describe the type of perspective used in the drawing on the next screen: Atmospheric, overlapping images, or diminishing sizes?

27. Perspective Diminishing sizes

28. Perspective A series of utility poles of the same size are a part of a one-point perspective drawing. Suppose the second utility pole in the drawing is 3.2 cm. tall and 1.6 cm. from the vanishing point. The distance between the utility poles is 4 cm. Use the proportion for a line of congruent objects to determine the height of the first utility pole.

29. x

30. Perspective 11.2 cm

31. Perspective An artist is using a one-point perspective to draw a line of Boeing 767 airliners parked along a runway. The first Boeing 767 in the line is to be 9 cm tall, and the last Boeing 767 is to be 1.6 cm tall. If the last Boeing 767 is drawn 7 cm from the vanishing point, how far from the last Boeing 767 should he draw the first Boeing 767 airliner?

32. Perspective 39.375 cm

33. The Golden Ratio Give the approximate value for the Golden Ratio. ________: 1

34. The Golden Ratio 1.62

35. The Golden Ratio Determine a point on a 28 inch ruler that divides the ruler into the Golden Ratio.

36. The Golden Ratio 17.3 inches

37. The Golden Ratio One dimension of a rectangle is 26 inches. If this rectangle is a Golden Rectangle, which of the following could be an approximation of the other dimension (in inches) of the rectangle? 15.07 in., 18.07 in., or 16.07 in.

38. The Golden Ratio 16.07 inches

39. The Golden Ratio If the width of a Golden Rectangle is 6 feet, what is its length?

40. The Golden Ratio 9.68 feet

41. The Golden Ratio If the length of a Golden Rectangle is 6 feet, what is its width?

42. The Golden Ratio 3.72 feet

43. Polygons and Stars What is the sum of the angle measures of a triangle?

44. Polygons and Stars 180o

45. Polygons and Stars Find the sum of the angle measures of a regular pentagon.

46. Polygons and Stars 540o

47. Polygons and Stars Find the measure of each angle of a regular pentagon.

48. Polygons and Stars 108o

49. Polygons and Stars If the measure of one exterior angle of a polygon is 18o, then this regular polygon has how many sides?

50. Polygons and Stars 20