




Slope  Parallel and Perpendicular Lines
Each topic includes lecture notes with an interactive demonstration, a video, and testing content.


How to Teach with these Materials

Motivation 

About 2,300 years ago, the Greek mathematician Euclid formalized the study of plane geometry by writing down its fundamental axioms, statements whose truth must be accepted as given. Euclid's fifth axiom is known as the Parallel Postulate. It states that if a line segment intersects two other lines in such a way that the sum of two adjacent interior angles (α and β in the diagram) is less than 180°, then the two other lines must meet (on that same side of the line segment). For most of the last 2,300 years, mathematicians have tried to determine whether the Parallel Postulate is truly independent of the first four axioms, with many incorrect "proofs" one way or the other being produced by very clever people. Finally, in 1868, the mathematician Eugenio Beltrami proved—correctly—that the Parallel Postulate is indeed independent of the first four axioms, and must therefore remain as an axiom of what has ever since been called Euclidean Geometry.










