MATH 6118-090
Non-Euclidean Geometry

Exercise Set #4

1. Use the Exterior Angles Theorem to give another proof of the uniqueness of a perpendicular dropped to a line from a point.

2. Prove that the sum of any two angles in a triangle is less than 180°. (Neutral geometry proof required.)

3. In the figure below, and are corresponding angles. Show that if and m are lines cut by a transversal t in such a way that two corresponding angles are congruent, then and m are parallel.

4. Prove that if is a triangle and the foot of the perpendicular from C to lies between A and B, then the angles and are both acute.