Formal Writing #3, due Wednesday, Feb. 27, in class:

Write a formal 2-4 page essay on the following topic.

Consider the following property of triangles: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another, then the two

triangles are congruent. This property is called “Side-Angle-Side” (SAS).

Is SAS true on the sphere? If you think it is true on the sphere, give a convincing argument that shows that it is true. If not, explain why it is false, and explain how you

could modify the statement to make it true on the sphere. Give a convincing argument that your modified statement is true.

You may assume that your reader is familiar with geometry on the plane (such as what one typically learns in high school) and knows that straight lines on the sphere are great circles. Unlike for Formal #2, I do ask that you write in standard academic prose. If it helps, you can imagine that you are writing this essay for a journal or magazine that introduces high school students to some advanced math concepts. (In that case, you can assume the journal or magazine already published your insightful essay on what is straight on a sphere, so the readers already understand that great circles are the straight lines on a sphere.)