You may use pencil, pens, protractor, ruler, compass and scissors on this test. You may not use a calculator, book or notes. Please take your time on each problem and show your work in the space provided. If you get stuck on a problem, move on to the next and return when you have time.
In spherical geometry, the sum of the measures of the interior angles of a triangle isa) less than 180°.
a) (20 points) One choice of A and B is shown below. Circle the points that would belong to L(AB) in this example.
An equivalent question phrased as a story problem: Your job is at location A and your spouse's job is at location B. You are about to buy a home together. You've agreed that your new home will be the same taxicab distance from each of your workplaces. Circle all the points that are possible locations for your new home.
b) (10 points) A friend of yours suggests that you define L(AB) (the set of possible locations of your new home) to be the perpendicular bisector of segment AB. Is this a good idea? Write a paragraph supporting your answer. (Answers that reveal an understanding of why this might be a good idea will receive more credit.)