Course Outline
These topics comprise the material normally taught in a high school Geometry course.
These topics comprise the material normally taught in a high school Geometry course.
- Chapter 1: Introduction to Geometry
Lines, Angles, Polygons, Polyhedra, Constructions - Chapter 2: Deductive Reasoning
Conditional Statements, Definitions, Direct and Indirect Proof, Geometry as a Deductive System, Famous Geometry Theorems - Chapter 3: Lines and Angles
Number Operations from Algebra, Rulers and Distance, Protractors and Angles, Bisection, Complementary and Supplementary Angles, Linear Pairs, Vertical Angles, Perpendicular Lines, Parallel Lines - Chapter 4: Congruence
Coordinates and Distance, Congruent Polygons, ASA Congruence, SAS Congruence, Proofs involving Congruence, Isosceles Triangles, Equilateral Trianges, SSS Congruence, Constructions - Chapter 5: Inequalities
Properties of Inequality, The Exterior Angle Theorem, Triangle Side and Angle Inequalities, The Triangle Inequality Theorem - Chapter 6: Parallel Lines
Line Symmetry, Parallel Lines, The Parallel Postulate, Angles formed by Parallel Lines, The Angles of a Triangle, AAS Congruence, HL Congruence - Chapter 7: Quadrilaterals
Quadrilaterals, Parallelograms, Point Symmetry, Rectanbles, Rhombuses, Squares, Trapezoids, The Midsegment Theorem - Chapter 8: Transformations
Transformations, Reflections, Isometries, Congruence, Symmetry - Chapter 9: Area
Areas of Squares and Rectangles, Areas of Triangles, Parallelograms and Trapezoids, The Pythagorean Theorem - Chapter 10: Similarity
Ratios and Proportions, Similar Figures, the Side-Splitter Theorem, AA Similarity, Dilations, Perimeters and Areas of Similar Figures - Chapter 11: Right Triangles
Proportions in Right Triangles, The Pythagorean Theorem, Isosceles Right Triangles, 30-60-90 Triangles, The Tangent Ratio, Sine and Cosine, Slope, The Law of Sines, The Law of Cosines - Chapter 12: Circles
Circles, Radii, Chords, Tangents, Central Angles, Arcs, Inscribed Angles, Secant Angles, Tangent Segments, Intersecting Chords - Chapter 13: The Concurrence Theorems
Triangles and Circles, Cyclic Quadrilaterals, Incircles, The Centroid, Ceva's Theorem, Napoleon's Discovery - Chapter 14: Regular Polygons and the Circle
Regular Polygons, Perimeter and Area of Regular Polygons, Polygons and Pi, The Area of a Circle, Sectors and Arcs - Chapter 15: Geometric Solids
Lines and Planes in Space, Solid Geometry, Rectangular Solids, Prisms, The Volume of a Prism, Pyramids, Cylinders and Cones, Spheres, Similar Solids, The Regular Polyhedra