1. a. Describe the two ways we discussed for defining 2. a. Suppose you fold a paper circle in half and then or thinking about the concept of angle Explain in thirds, so that the layers fold onto each other how those two definitions of angle are related. and make identical copies of an angle, as in b. The two angles in Figure 10.72 are each 20", Figure 10.73. What will the size of that angle be Explain what it means for an angle to be 20 in degrees! Explain! and discuss how both of those angles can be the h. For each of the following angles, describe how same size even though one might look bigger to fold a circle to create the angle and explain than the other. why your method will create that angle. I. 180 ii. 90 fil. 459 Figure 10.72 Fold into Fold into 1apal parts Figure 10.73 3. Sec Figure 10.74. C. Prove that the sum of the angles in every trian- a. Given that the lines marked with arrows are gle is always 180" in two ways by applying the parallel and that a = 60 and 5 = 140", explain Parallel Postulate and by using the idea of walk- how to determine angle e without measuring it. ing and turning all the way around a triangle. b. Now suppose you didn't know specific values 5. Explain how to determine the sum of the angles for amples a and & Find and explain an equa- otb+c+dte+ /+ : in the 7-gon in Fig- Lion relating a, b. and c. ure 10.75 without measuring the angles. See if you can find three different explanations for how to determine this sum! Figure 10.74 Figure 10.75 4. a. Describe an informal hands on way to help stu- 6. How is the length of the shadow that a pole casts dents see why it is plausible that the sum of the on horizontal ground related to the angle that the angles in a triangle is 180. sun's rays make with the ground? When the shadow b. Give at least two reasons why the method of is longer, is the angle greater or smaller than when part (a) is not a proof that the sum of the angles the shadow is shorter? Make math drawings to in every triangle is always 180' help you explain your