Foundations of Geometry
A proof-based course in geometry, beginning from axioms for plane geometry. We will also look at properties involving distance, angles, triangles, quadrilaterals, and circles, as well as Euclidean and non-Euclidean geometry.
Day 1 - Introduction
FREE PREVIEWDay 2 - Logic and Methods of Proof
Day 3 - Axiomatic Systems and Incidence Geometry
Day 4 - Incidence Geometry Theorems and Proofs
Day 5 - Plane Geometry
Day 6 - Metrics
Day 7 - Half-Planes and Angles
Day 8 - Crossbar Theorem, Linear Pair Theorem, and Perpendiculars
Day 9 - Side-Angle-Side Congruence
Day 10 - Parallel Postulates and Neutral Geometry
Test 1
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Day 11 - Triangle Congruence
Day 12 - Inequalities for Triangles
Day 13 - Parallel Lines and Angles Sums for Triangles
Day 14 - Quadrilaterals
Day 15 - Equivalence to Euclidean Parallel Postulate
Day 16 - Rectangles
Day 17 - Existence of Rectangles
Day 18 - Euclidean Geometry
Day 19 - Pythagorean Theorem and Trigonometry
Test 2
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