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that the exterior angle BCD is greater than ZBAC. Using a similar construction on the other side of the triangle, we can also prove that BCD is greater than LCBA. But it is known that EAT does not hold for an arbitrary triangle in spherical geometry, thus the previous proof may not work for some triangles on sphere. SUBMISSION You will submit a robust construction of proof for EAT in spherical geometry and a screencast presentation explaining when the construction in spherical geometry works or fails. 1. GEX Construction of EAT Proof in Spherical Geometry Note that this construction works in Euclidean geometry (even without Euclid's fifth postulate) but does not work in spherical geometry. In this problem, provide a GEX construction illustrated in the previous page in spherical geometry. 2. Screencast Presentation of Counter-Example in Spherical Geometry After creating your construction above, look for such cases when the proof does not work. As you drag around stretch them far apart the three vertices of AABC and stretch them far apart, you will see in some cases that ZBCD is NOT greater than ZCBA. Create a screencast presentation to show such cases and explain when the construction works or not. You need to be specific in describing when the construction fails in terms of what would be a condition that the construction works or fails.