Chapter 1: An Introduction to Geometry
- Definitions: point, line, plane, ray, angle, etc.
- Perimeter and area
Chapter 2: The Nature of Deductive Reasoning
- Conditional (if-then) statement, converse
- Direct and indirect proof
- Deductive system
- Pythagorean Theorem & Triangle Sum Theorem
Chapter 3: Lines and Angles
- Algebraic postulates
- Ruler & distance
- Protractor & angle measure
- Bisection
- Complementary & supplementary angles
- Linear Pairs & Vertical angles
- Perpendicular & parallel Lines
Chapter 4: Congruence
- Distance Formula
- Polygons and congruence
- ASA, SAS, SSS congruence
- Congruence Proofs
- Isosceles & Equilateral Triangles
Chapter 5: Inequalities
- Properties of inequality
- Triangle inequalities
- Exterior angle theorem
Chapter 6: Parallel Lines
- Proving lines parallel
- Parallel lines and angles
- Angle Sum Theorem
- inverses and contrapositives
- indirect proof
- AAS, HL congruence
Chapter 7: Quadrilaterals
- Parallelograms
- Rectangles, rhombuses, squares
- Trapezoids, midsegment theorem
Chapter 8: Transformations
- Transformations: isometries and dilation
- Isometries and congruence
- Transformations and symmetry
Chapter 9: Area
- Area – square, rectangle, triangle, parallelogram, trapezoid
- Pythagorean theorem
Chapter 10: Similarity
- Ratio and proportion
- Similar figures
- Side-splitter, AA similarity theorems
- Perimeters & areas of similar figures
Chapter 11: The Right Triangle
- Proportions in a right triangle
- Pythagorean theorem revisited
- Special right triangles
- Tangent, Sine, and Cosine ratios
- Slope
Chapter 12: Circles
- Definitions: circle, radius, chord etc.
- Tangents
- Central angles and arcs
- Inscribed angles
- Secant angles
- Tangent segments and Intersecting chords
If time allows:
Chapter 13: The Concurrence Theorems
- cyclic
- Lessons 1 – 4
Chapter 14: Regular Polygons and the Circle
- Regular polygons
- Area of a circle
- Sectors and arcs
Chapter 15: Geometric Solids
- Lines and planes in space
- Solid geometry as a deductive system
- Rectangular solids
- Prisms, volume of a prism
- Pyramids, cylinders, cones
- Spheres