Topics in Geometry

This set of lessons assumes mastery of the content from Algebra I. This is not a full course in Geometry. Instead, it offers the essential geometric concepts and maturation of mathematical thinking that is required for success in Algebra II, Precalculus and Calculus. A strong emphasis in ‘Topics in Geometry’ is on logic, proof, and proof techniques.

1. Beginning Terminology, Points, Lines, and Planes 2. Segments, Rays, Angles 3. Introduction to Polygons 4. Interior and Exterior Angles in Polygons 5. Quadrilaterals 6. ‘If ... Then ...’ Sentences 7. Contrapositive and Converse 8. Proof Techniques 9. Logical Equivalences and Practice with Truth Tables 10. Applying Logical Equivalences to Algebraic and Geometric Statements 11. Constructions 12. Introduction to the Two-Column Proof 13. The Pythagorean Theorem 14. More Terminology for Segments and Angles 15. Angles: Complementary, Supplementary, Vertical, and Linear Pairs 16. Equivalence Relations 17. Triangle Congruence 18. Relationships between Angles and Sides in Triangles 19. Practice with Two-Column Proofs 20. Is there an ‘SSA’ Congruence Theorem? No! 21. More on Exterior Angles in Triangles 22. Parallel Lines 23. Parallelograms and Negating Sentences 24. Introduction to Area and Perimeter 25. Area Formulas: Triangle, Parallelogram, Trapezoid 26. Similarity, Ratios, and Proportions 27. Perimeters and Areas of Similar Polygons 28. Two Special Triangles