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Geometry: Rules, Theorems, Postulates, Corollaries and Formulas


Set Theory
Points, Lines, Planes
Planes and Space
Tangents and Secants
Chords, Power Point
Congruent Triangles
Congruent Polygons
Congruency Proofs
Congruent Circles, Arcs
Similarity Proofs
Pythagorean Theorem
Symmetry and Transformations
Analytic Geometry
Coordinate Proofs
Non-Euclidean Geometry
Rules Postulates Theorems
Morleys Theorem

In most areas of math, special rules are used to help solve problems. This section lists many of these rules such as definitions, postulates, theorems, corollaries and formulas that are used in geometry. Certain ones are especially important to know when doing a geometry proof. To help with finding a particular geometry rule, the rules are placed in their most appropriate category and are listed alphabetically.

The rules are described in their area of geometry that follows. The basic category lists geometry rules for lines, planes, angles, other simple geometric figures and their relationships.

Basic Triangles Polygons with Quadrilaterals Circles
Solids Formulas and Concepts Slope Transformations

The rules of geometry are also listed in alphabetical order with links to their description.

30-60-90 Equilateral Triangle Corollary
30-60-90 Right Triangle Theorem
45-45-90 Triangle
Acute Complementary Angles Theorem
Alternate Exterior Angles Corollary
Alternate Exterior Angles Theorem
Alternate Interior Angles Corollary
Alternate Interior Angles Theorem
Altitudes Concurrency Theorem
Angle Addition Postulate
Angle Bisector Points Postulate
Angle Bisector Theorem
Angle Bisector Theorem
Angle Bisectors Concurrency Theorem
Angle Measure
Angle-Angle or AA Similarity Postulate
Angle-Angle-Angle or AAA Similarity Theorem
Angle-Angle-Side or AAS Congruence Theorem
Angle-Side-Angle or ASA Congruence Postulate
Arc Addition Postulate
Arc Length Theorem
Area Addition Postulate
Area Postulate
Cavalieriís Principle
Central Angle Postulate
Cevaís Theorem
Chord Bisector Theorem
Chord Distance Congruency Theorem
Chord Line Segment Products Theorem
Chord Midsegment Theorem
Chord Tangent Theorem
Circle Area
Circle Circumference
Circle General Form Equation
Circle Standard Form Equation
Circumscribed Inscribed Polygon
Complement or Supplementary
Complementary Angles
Cone Base Area
Cone Cross Section Ratio Theorem
Cone Cross Sections
Cone Lateral Area
Cone Pythagorean Theorem
Cone Surface Area
Cone Volume Theorem
Congruent Arc Angles
Congruent Central Angles
Congruent Inscribed Angles Theorem
Congruent Tangent Line Segments Theorem
Congruent Triangle Area Postulate
Consecutive Exterior Angles
Consecutive Interior Angles Corollary
Consecutive Interior Angles Theorem
Converse 30-60-90 Right Triangle Theorem
Converse 45-45-90 Triangle
Converse Chord Bisector Theorem
Converse Hinge Theorem
Converse Isosceles Right Triangle Theorem
Converse Parallelogram Opposite Angles Theorem
Converse Parallelogram Opposite Sides Theorem
Converse Pythagorean Theorem
Converse Tangent Plane Perpendicular Sphere Theorem
Converse Triangle Proportionality Theorem
Corresponding Angles Postulate
Corresponding Angles Theorem
Corresponding Parts Triangle SAS Similarity Theorem
Corresponding Sides Triangle SSS Similarity Theorem
Corresponding to Alternate Interior Angles Theorem
Cube Diagonal Corollary
Cube Volume Corollary
Cyclic Polygon
Cylinder Base Area
Cylinder Cross Sections
Cylinder Lateral Area
Cylinder Surface Area
Cylinder Volume Theorem
Dilation Theorem
Distance Postulate
Equal Volume Pyramids
Equiangular Triangle Angle Measures
Equiangular Triangle Corollary
Equidistant Point To Angle Postulate
Equidistant Point To Line Segment Postulate
Equilateral Triangle Area Theorem
Equilateral Triangle Corollary
Euler Polyhedron Formula
Exterior Angle Inequality Theorem
Exterior Angles Corollary
Exterior Intersection Theorem
First Minimum Theorem
Heronís Theorem
Hinge Theorem
Inscribed Angle Theorem
Inscribed Quadrilateral
Inscribed Right Angle Theorem
Intersecting Lines Plane
Intersecting Lines Postulate
Intersecting Perpendicular Line Theorem
Intersecting Planes Postulate
Isometry Preservation
Isosceles Right Triangle Corollary
Isosceles Right Triangle Theorem
Isosceles Trapezoid Base Angles
Isosceles Trapezoid Diagonals
Isosceles Triangle Bisector Theorem
Isosceles Triangle Theorem
Kite Opposite Angles
Line Circle Theorem
Line Intersecting A Plane
Line Postulate
Line Projection
Line Segment Length
Line Segment Slope Theorem
Linear Pair Right Angles
Lines Perpendicular Plane Theorem
Median Concurrency Theorem
Midpoint Formula
Midpoint Postulate
Midsegment Theorem
Minor Arc Chord Congruency Theorem
Parallel Intersection
Parallel Line Arcs
Parallel Lines Distance
Parallel Planes Distance
Parallel Planes Perpendicular Transversal
Parallel Planes Transversal
Parallel Postulate
Parallel Slopes Postulate
Parallelogram Area
Parallelogram Consecutive Angles Theorem
Parallelogram Diagonal Congruent Triangle Theorem
Parallelogram Diagonals Theorem
Parallelogram Diagonals Theorem
Parallelogram Obtuse Angle
Parallelogram One Pair Opposite Sides Theorem
Parallelogram Opposite Angles Theorem
Parallelogram Opposite Sides Theorem
Parallelogram Right Angle
Perpendicular Bisecting Plane Theorem
Perpendicular Bisector Points Postulate
Perpendicular Bisector
Perpendicular Bisectors Concurrency Theorem
Perpendicular Line Collinear Point Theorem
Perpendicular Line Non-Collinear Point Theorem
Perpendicular Lines Theorem
Perpendicular Plane Theorem
Perpendicular Planes Intersection Theorem
Perpendicular Quadrilateral Diagonals
Perpendicular Slopes Postulate
Perpendicular Transversal Corollary
Perpendicular Transversal Theorem
(π) Pi
Plane Angles Theorem
Plane Circle Intersect Theorem
Plane Distance Formula
Plane Perpendicular Lines Theorem
Plane Postulate
Plane Traversal
Point Perpendicular Line
Point Perpendicular Plane
Point Slope Formula
Points In Space
Points In The Plane
Points On The Line
Points Reflection Theorem
Polygon Area Ratio Theorem
Polygon Central Angle
Polygon Diagonal Number
Polygon Exterior Angle Measure
Polygon Exterior Angles
Polygon Interior Angle Measure
Polygon Interior Angles
Prism Base Areas
Prism Cross Sections
Prism Lateral Area
Prism Lateral Faces
Prism Surface Area
Proportional Arcs
Proportional Perimeters Theorem
Protractor Postulate
Pyramid Base Area
Pyramid Cross Section Ratio Theorem
Pyramid Cross Sections
Pyramid Lateral Area
Pyramid Surface Area
Pyramid Volume Theorem
Pythagorean Inequality Theorem
Pythagorean Theorem
Quadrilateral Interior Angles
Quadrilateral Parallelogram Theorem
Radii Corollary
Radius Bisector Theorem
Rectangle Area
Rectangle Diagonals Theorem
Rectangle Parallelogram Theorem
Rectangle Right Angles
Regular Polygon Apothem
Regular Polygon Area Theorem
Regular Polygon Perimeter
Regular Polygon Radius
Regular Pyramid Apothem Pythagorean Theorem
Regular Pyramid Radius Pythagorean Theorem
Rhombus Area
Rhombus Diagonal Bisector Theorem
Rhombus Diagonal Quadrilateral
Rhombus Diagonals Theorem
Rhombus Parallelogram Theorem
Rhombus Sides
Right Angles Theorem
Right Or Obtuse Angle Measure
Right Or Obtuse Triangle
Right Prism Volume Postulate
Right Rectangular Prism Diagonal Length Theorem
Right Rectangular Prism Volume Corollary
Right Triangle Altitude Geometric Mean
Right Triangle Altitude
Right Triangle Area
Right Triangle Congruent Hypotenuse And Angle
Right Triangle Congruent Hypotenuse And Leg
Right Triangle Congruent Leg And Angle
Right Triangle Congruent Legs
Right Triangle Leg Geometric Mean
Right Triangle Median
Rigid Motion Theorem
Rotation Postulate
Ruler Postulate
Secant Line Segment Products Theorem
Secant Tangent Line Segment Products Theorem
Secant Tangent Theorem
Second Minimum Theorem
Sector Area Ratio
Sector Area
Segment Addition Postulate
Side-Angle-Side or SAS Congruence Postulate
Side-Side-Side or SSS Congruence Postulate
Similar Triangle Area Ratio
Slope Formula
Slope Intercept Equation
Space Distance Formula
Sphere Chord Bisector Theorem
Sphere Chord Midpoint Theorem
Sphere Surface Area Theorem
Sphere Volume Theorem
Square Area Corollary
Square Sides
Sum of Acute Angles
Sum of Remote Interior Angles
Sum of Triangle Angles
Supplement Postulate
Supplementary Angles
Surface Area Ratio Theorem
Symmetry Perpendicular Lines
Tangent Line Theorem
Tangent Perpendicular Radius Theorem
Tangent Plane Perpendicular Sphere Theorem
Third Angle Theorem
Three Parallel Lines Parallel Transversals
Three Parallel Lines Transversals
Three Parallel Lines
Three Points Postulate
Transitive Congruent Triangles
Trapezoid Area
Trapezoid Base Angles
Trapezoid Diagonals
Trapezoid Median
Triangle Altitude Theorem
Triangle Area Corollary
Triangle Area Corollary
Triangle Base Height Area Theorem
Triangle Inequality Theorem
Triangle Isometry
Triangle Median Theorem
Triangle Proportionality Theorem
Triangle Radius Perimeter Area Theorem
Triangle Side Length Theorem
Triangle Similarity Theorem
Two Angles Theorem
Two Circles Theorem
Two Intersecting Chords Theorem
Two Intersecting Secants Theorem
Two Parallel Lines
Two Perpendicular Lines to Plane
Two Points In A Plane
Unequal Angles Theorem
Unequal Arc Measures
Unequal Central Angles
Unequal Chords
Unequal Sides Theorem
Vertical Angles Theorem
Volume Postulate
Volume Ratio Theorem

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