Assignment:
Q1. Forest rangers use degree measures to identify directions and locate critical spots such as fires. In the following drawing, a forest ranger at tower A observes smoke at a bearing of 149° (clockwise from the north), while another forest ranger at tower B observes the same source of smoke at a bearing of 250° (clockwise from the north).
a. Choose two locations for A and B and use a protractor and a straightedge to locate the source of the smoke.
b. Explain how the forest rangers could find the location of the fire.
c. Describe other situations in which location can be determined by similar methods.
Q2. A student says that it is actually impossible to measure an angle, since each angle is the union of two rays that extend infinitely and therefore continue forever. What is your response?
Q3. One student says, "My sister's high school geometry book talked about equal angles. Why don't we use the term `equal angles' instead of 'congruent angles'?" How do you reply?
Q4. A student asks what exactly Euclidean geometry is. How do you answer?
Q5. Draw each of the following curves:
a. A simple closed curve
b. A closed curve that is not simple
c. A concave hexagon
d. A convex decagon
Q6. Sketch each of the following:
a. Three planes that intersect in a point
b. A plane and a cone that intersect in a circle
c. A plane and a cylinder that intersect in a semen
Q7. If Angle ACB is a right angle as shown, and the other angles are as indicated in the figure, find x, the measure of Angle DCB.
Q8. If a cube intersects a plane, what possible figures can be obtained by the intersection? Sketch the planes and figures obtained in each case.
Q9. If a pyramid has an octagon for a base, how many lateral faces does it have?
Q10. If one is drawing a two-dimensional representation of a large n x n x n cube, will the edges of the square faces appear parallel as they do in a normal square on a piece of paper? Why or why not?
Q11. Explain whether or not a cylinder has to have a circular base.
Provide complete and step by step solution for the question and show calculations and use formulas.