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#### Geometry Building Blocks

FREEGeometry building blocks reviews elementary concepts on the subject, including the definition of terms related to shapes like lines, angles, triangles, polygons, and circles. Topics include:

- Three Undefined Terms: Point, Line, and Plane
- Counterexample
- Writing a Good Definition
- Postulate, Axiom, Conjecture
- Converse
- Line Segments
- Rays
- Parallel and Skew Lines
- Midpoints and Congruent Segments
- Parallel Planes and Lines
- Vertex and Diagonals
- Calculating the Midpoint
- Angles: Types and Labeling
- Using a Protractor
- Angle Bisectors
- Supplementary and Complementary Angles
- Polygons
- Types of Triangles
- Perimeter
- Parts of a Circle

#### Reasoning, Diagonals, Angles and Parallel Lines

Reasoning, diagonals, angles and parallel lines covers applications of both inductive and deductive reasoning to geometry, as well as the definitions on angles and parallel lines. Topics include:

#### Constructions

Constructions covers elementary methods related to perpendicularity, parallelism, bisectors, angles, polygons, circles and centers of a triangle. Topics include:

- Duplicating a Line Segment
- Duplicating an Angle
- Constructing the Perpendicular Bisector
- Constructing a Perpendicular to a Line
- Constructing an Angle Bisector
- Constructing Parallel Lines
- Constructing Altitudes
- Constructing a Median
- Constructing a Triangle Midsegment
- Point of Concurrency
- Circumscribed and Inscribed Circles and Polygons
- Constructing the Incenter
- Constructing the Circumcenter
- Constructing the Orthocenter
- Constructing the Centroid
- Constructing a Perpendicular at a Point on a Line

#### Triangles

Triangles covers basic definitions and theorems, including the relationships between sides and angles, as well as the properties of isosceles triangles. Topics include:

#### Polygons

Polygons covers terms and formulas related to common polygon shapes, specially those of quadrilaterals such as: squares, rectangles, trapezoid, rhombus, parallelograms. Topics include:

#### Circles

Circles covers terms and formulas, including central and inscribed angles, and the relationships between tangents, arcs, secants, chords and circumference. Topics include:

- Locus and Definition of a Circle and Sphere
- Central Angles and Intercepted Arcs
- Chords and a Circle's Center
- Radii to Tangents
- Tangent Segments to a Circle
- Inscribed Angles
- Angles in Semicircles and Chords to Tangents
- Cyclic Quadrilaterals and Parallel Lines in Circles
- Circumference
- Arc Length
- Secants

#### Transformations

Transformations covers the practice of geometric transformations, involving reflections, rotations and translations, among others. Topics include:

#### Area

Area covers formulas related to common shapes, such as triangles, quadrilaterals, polygons, circles, and the surfaces of some 3D shapes. Topics include:

- Area of Parallelograms
- Area of Triangles
- Area of Trapezoids
- Solving Formulas
- Area of Kites and Rhombuses
- Center and Apothem of Regular Polygons
- Area of Regular Polygons
- Area of Circles
- Area of a Sector
- Area of a Segment
- Area of an Annulus
- Regions Between Circles and Squares
- Surface Area of Prisms
- Surface Area of Cylinders
- Surface Area of Pyramids
- Surface Area of Cones
- Surface Area of Joined Solids

#### Pythagorean Theorem

FREEPythagorean theorem covers proofs, formulas and applications related to this often used theorem. Topics include:

- Pythagorean Theorem Proofs
- Square Root Operations
- Using the Pythagorean Theorem to find a Missing Hypotenuse
- Using the Pythagorean Theorem to find a Missing Leg
- Space Diagonals
- Converse of the Pythagorean Theorem
- 45-45-90 Triangles
- 30-60-90 Triangles
- Distance Formula
- Equation of a Circle
- Calculating Coordinates in the Unit Circle

#### Volume

Volume covers terms and formulas related to 3D shapes, particularly those of prisms and cylinders. Topics include:

#### Similarity

Similarity covers how to solve basic proportions, the properties of similarity, similarity shortcuts and the how to use area and volume ratios to find missing information. Topics include:

- Solving Proportions
- Properties of Similar Polygons
- Similarity Shortcuts
- Similar Triangles in Circles and Right Triangles
- Indirect Measurement
- Proportional Segments Between Parallel Lines
- Corresponding Parts of Similar Triangles
- Angle Bisectors and Opposite Side Ratios
- Similarity and Area Ratios
- Similarity and Volume Ratios

#### Basic Trigonometry

Basic trigonometry covers the definitions and formulas for the basic trigonometric ratios, as well as the fundamental theorems and some applications Topics include: