By Harold Levine
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Extra info for Classifying Immersions into IR4 over Stable Maps of 3-Manifolds into IR2
Multiple Choice Use the angle measures to determine which of the following shapes is a parallelogram. The shapes may not be drawn to scale. A. 128° 52° C. 52° 128° 120° 60° B. 110° 70° 75° 105° D. qxd 3/14/05 3:48 PM Page 47 25. How did you know which shape was a parallelogram in Exercise 24? 26. Liang said that an equilateral triangle must have angles totaling 3608 because he can cut it into two right triangles, as in the diagram. Is Liang’s statement correct? Explain. 30° 30° 60° 90° 90° 60° Connections 27.
11. Sun Sun Hive Hive Flowers 12. Flowers 13. qxd 3/14/05 3:47 PM Page 43 14. Draw an angle for each measure. Include a curved arrow indicating the turn. a. 458 b. 258 c. 1808 d. 2008 15. Without measuring, decide whether the angles in each pair have the same measure. If they do not, tell which angle has the greater measure. Then find the measure of the angles with an angle ruler to check your work. a. 1 2 b. 1 2 c. qxd 3/15/05 8:04 AM Page 44 16. Estimate the measure of each angle, then check your answers with an angle ruler.
B. On the “new” half of the figure, what are the coordinates of the point that corresponds to point A? What are the coordinates of the point that corresponds to point B? c. Describe some properties of the polygon. qxd 3/14/05 3:48 PM Page 50 40. Multiple Choice Which choice is a 1808 rotation of the figure below? F. G. H. J. Extensions 41. Design a new polar coordinate grid for playing Four in a Row. Play your game with a friend or a member of your family. Explain the ideas that led to your new design.
Classifying Immersions into IR4 over Stable Maps of 3-Manifolds into IR2 by Harold Levine