Answer the following parts in Plane Geometry: (a) Show that theconverse to the alternate interior angles theorem postulate impliesthe angle sum postulate in Plane Geometry. (Hint: Check out EuclidBook 1 Prop 32 for the idea, but make sure you write an axiomaticPlane Geometry argument.) (b) Show that the angle sum postulateimplies the converse to the alternate interior angles theorem.(Hint: Draw a perpendicular.) (c) Explain why that means you canconclude that the two statements are equivalent to each other inPlane Geometry.
