Table of Contents
-
Foundations of Geometry
- Points, Lines, and Planes in Space
- Congruence of Line Segments
- Distance and Midpoint on a Number Line
- Distance on the Coordinate Plane: Pythagorean Formula
- Midpoint on the Coordinate Plane
- Measuring Angles
- Turns and Angles
- Complementary and Supplementary Angles
- Adjacent and Vertically Opposite Angles
- Vertically Opposite Angles
- Lines and Transversals: Angle Pairs
- Parallel Lines and Transversals: Angle Relationships
- Parallel Lines and Transversals: Angle Applications
- Nets of 3D Shapes
- Convex and Concave Polygons
- Reasoning and Proof
- Parallel and Perpendicular Lines
- Transformations
- Congruence
-
Triangle Relationships
- Angle Sum of a Triangle
- Isosceles Triangle Theorems
- Equilateral Triangles
- Triangles on the Coordinate Plane
- Perpendicular Bisector Theorem and Its Converse
- Medians of Triangles
- Exterior Angles of a Triangle
- Inequality in One Triangle: Angle Comparison
- Inequality in One Triangle: Side Comparison
- The Hinge Theorem
- Angle Bisector Theorem and Its Converse
-
Right Triangles and Trigonometry
- The Pythagorean Theorem
- The Converse of the Pythagorean Theorem
- Pythagorean Inequality Theorem
- The Cosine Ratio
- The Sine Ratio
- The Tangent Ratio
- Right Triangle Trigonometry: Solving for an Angle
- Right Triangle Trigonometry: Solving for a Side
- Angles of Elevation and Depression
- Right Triangle Altitude Theorem
- Applications on the Pythagorean Theorem
- Special Right Triangles
- Trigonometric Ratios of Special Triangles
- Finding the Area of a Triangle Using Trigonometry
- Law of Sines
- Law of Cosines
- Applications on Sine and Cosine Laws
-
Quadrilaterals and Polygons
- The Sum of Angles in Quadrilaterals
- Interior Angles of a Polygon
- Exterior Angles of a Polygon
- Properties of Rectangles
- Rectangles on the Coordinate Plane
- Classifying Quadrilaterals
- Properties of Rhombuses
- Properties of Squares
- Properties of Kites
- Properties of Parallelograms
- Parallelograms on the Coordinate Plane
- Perimeter of Polygons
- Isosceles Trapezoids
- Trapezoid Midsegment Theorem
- Similarity
-
Area, Surface Area, and Volume
- Areas of Rectangles and Squares
- Area of a Parallelogram
- Area of a Triangle
- Volumes of Rectangular Prisms and Cubes
- Volumes of Cylinders
- Surface Areas of Rectangular Prism and Cubes
- Surface Areas of Cylinders
- Area of a Trapezoid
- The Area of a Square in terms of Its Diagonals
- Finding the Area of a Rhombus Using Diagonals
- Area of a Kite
- Arc Lengths
- Areas of Composite Figures
- Areas of Regular Polygons
- Areas of Similar Polygons
- Plans and Elevations
- Surface Areas of Prisms
- Surface Areas of Cones
- Volumes of Oblique Prisms
- Volumes of Triangular Prisms
- Volumes of Triangular and Quadrilateral Pyramids
- Surface Areas of Pyramids
- Volumes of Cones
- Volumes of Composite Solids
- Volumes of Spheres
- Surface Areas of Spheres
- Volumes of Composite Prisms
- Surface Areas of Composite Solids
- Relating Volumes and Surface Areas
- Similarity of Solids
- Density of Solids
-
Circles
- Circles
- Areas and Circumferences of Circles
- Central Angles and Arcs
- Perpendicular Bisector of a Chord
- Inscribed Angles in a Circle
- Properties of Cyclic Quadrilaterals
- Tangents of a Circle
- Properties of Tangents and Chords
- Circumscribed Polygons
- Angles of Intersecting Lines in a Circle
- Angles of Tangency
- Equation of a Circle
- Equation of a Circle Passing through Three Noncollinear Points
- Special Segments in a Circle
- Areas of Circular Segments