Mathematics Homework Help

Angle-Side-Angle (ASA): If one side and the adjacent angles of one triangle are congruent to one side and the adjacent angles of the other triangle, then the two triangles are congruent.

1. Give a counterexample that shows ASA is not true for all triangles on the surface of the sphere. Explain why the counterexample exists. Clearly label the angles and sides of your counterexample and shade the triangles.
2. Pick a definition of the small triangle (it is your choice which definition you want to use, but only choose one definition and state which definition you pick) and explain why ASA is true for small triangles on the sphere (where small is defined by the definition you picked).
3. Explain why ASA is true on the plane for all triangles.
4. use your own words, do not use cos law, you need to use the 3 definitions of the small triangles on the sphere, and provide clear diagrams.
5. Three different definitions of “small triangle”. ”
   Def 1: A triangle on the sphere is small if all angles are less than 180
   degrees Def 2: A triangle on the sphere is small if all sides are less than ½ of a
   great circle Def 3: A triangle on the sphere is small if it is contained in a
   hemisphere