High School Geometry

A typical high school geometry syllabus will vary depending on the specific curriculum (e.g., Common Core, state standards, or international programs like IGCSE or IB), but here are some commonly covered topics.

The following diagram gives a compilation of essential formulas for high school geometry.

 

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High School Geometry Topics

• Geometry Terms

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

• Triangle Theorems & Polygons

  Triangle Theorems
  Triangle Angle Sum
  Isosceles Triangles
  Triangle Side Inequalities
  Triangle Side & Angle Inequalities
  Remote Interior Angles
  
  Congruent Triangles
  SSS & SAS
  ASA & AAS
  Hypotenuse Leg (HL)
  Why SSA & AAA Don’t Work as Congruence Shortcuts
  
  Similar Triangles & Polygons
  Solving Proportions
  Properties of Similar Polygons
  Similarity Shortcuts
  Similar Triangles in Circles & Right Triangles
  Indirect Measurement
  
  Similar Polygons
  Proportional Segments Between Parallel Lines
  Corresponding Parts of Similar Triangles
  Angle Bisectors & Opposite Side Ratios
  Similarity & Area Ratios
  Similarity & Volume Ratios

• Diagonals in a Polygon

  Diagonals
  Number of Diagonals in a Polygon
  Number of Handshakes at a Party

• Angles & Parallel Lines

  Angles
  Adjacent Angles
  Vertical Angles
  Corresponding Angles
  
  Parallel Lines
  Alternate Interior Angles
  Alternate Exterior Angles
  Same Side Interior & Same Side Exterior Angles
  Converse of Parallel Lines Theorem

• Angles & Properties of Polygons

  Angles of Polygons
  Polygon Angle Sum
  Equiangular Polygon Sums
  Exterior Angles of a Polygon
  
  Properties of Polygons
  Kite Properties
  Trapezoid Properties
  Triangle Midsegment Properties
  Trapezoid Midsegment Properties
  
  Properties of Polygons
  Parallelogram Properties
  Trapezoid Arch & Panel Design Problem
  Rhombus Properties
  Rectangle & Square Properties

• Area of 2-D Shapes

  Area Formulas
  Area of Parallelograms
  Area of Triangles
  Area of Trapezoids
  Solving Formulas
  
  Area of Polygons
  Area of Kites & Rhombuses
  Center & Apothem of Regular Polygons
  Area of Regular Polygons
  
  Area involving Circles
  Area of Circles
  Area of a Sector
  Area of a Segment
  Area of an Annulus
  Regions Between Circles & Squares

• Surface Area of Solids

  Surface Area
  Surface Area of Prisms
  Surface Area of Cylinders
  Surface Area of Pyramids
  
  Surface Area
  Surface Area of Cone
  Surface Area of Sphere
  Surface Area of Joined Solids

• Volume of Solids

  Volume
  3-D Solid Properties
  Volume of Prisms
  Volume of Cylinders
  Volume of Cones
  
  Volume
  Volume of Pyramids
  Solving Equations with Squares & Cubes
  Volume of Spheres
  Surface Area of Spheres

• Transformations & Symmetry

  Transformations
  Transformations & Isometries
  Translations
  Reflections
  Rotations
  Compositions of Transformations
  Glide Reflections
  
  Symmetry
  Reflectional Symmetry
  Rotational Symmetry
  Dilations

• Geometry Proofs & Reasoning

  Proofs
  CPCTC
  Two Column Proofs
  Flowchart Proofs
  Special Isosceles Triangle Properties
  
  Reasoning
  Inductive Reasoning
  Deductive Reasoning

• Constructions

  Constructions 1
  Duplicating a Line Segment
  Duplicating an Angle
  Constructing the Perpendicular Bisector
  Constructing a Perpendicular at a Point on a Line
  Constructing a Perpendicular to a Line
  
  Constructions 2
  Constructing an Angle Bisector
  Constructing Parallel Lines
  Constructing Altitudes
  Constructing a Median
  
  Constructions 3
  Constructing a Triangle Midsegment
  Point of Concurrency
  Circumscribed & Inscribed Circles & Polygons
  Constructing the Incenter
  
  Constructions 4
  Constructing the Circumcenter
  Constructing the Orthocenter
  Constructing the Centroid

• Circles, Tangents & Secants

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

• Pythagorean Theorem

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

• Basic Trigonometry

  Trigonometry
  Trigonometric Ratios: Sine
  Trigonometric Ratios: Cosine
  Trigonometric Ratios: Tangent
  Inverse Trigonometric Functions
  
  Application of Trigonometry
  Angle of Elevation & Depression
  Using Sine to Calculate the Area of a Triangle
  The Law of Sines
  The Law of Cosines

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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