2. in a spherical model of riemannian geometry, the sides of a triangle are arcs of great circles. assume here that the model is a sphere of radius 1 foot.
(a) choose a particular great circle (think of the equator) and mark off an arc b of length π feet. at each endpoint construct a perpendicular (geodesic) segment, and extend
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the two segments until they meet. (why must they meet? where will they meet? ) call that point c. what is the sum of the angles of ∆abc? is ∆abc equilateral? justify your answers.
(b) at point c, form an angle of 60o with ac as one side. extend the other side until it meets ab; call that point d. what is the sum of the angles of ∆acd? how long is ad? how long is cd?
(c) let m be the midpoint of ab. can you construct a triangle with base am that is similar to ∆abc? can you construct any other triangle that is similar but not congruent to ∆abc? explain.