ONE MATHEMATICAL CAT, PLEASE!
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