 ## Geometry Course Outline

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

• 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