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.

 

Geometry Worksheets
Use the following worksheets to practice your geometry skills.
Printable & Online Geometry Worksheets

Topics for High School Geometry

Basic Geometric Concepts
Three Undefined Terms
Point, Line, and Plane, Counterexample, Writing a Good Definition Postulate, Axiom, Conjecture
Lines
Line Segments, Rays, Parallel and Skew Lines
Midpoints & Congruent Segments
Calculating the Midpoint, Parallel Planes & Lines, Vertex & Diagonals

Angles
Angles
Types & Labeling, Using a Protractor, Angle Bisectors, Supplementary & Complementary Angles
Angles Relationships
Adjacent Angles, Vertical Angles, Corresponding Angles
Angles & Parallel Lines
Alternate Interior Angles, Alternate Exterior Angles, Same Side Interior & Same Side Exterior Angles, Converse of Parallel Lines Theorem
Angles of Polygons
Polygon Angle Sum, Equiangular Polygon Sums, Exterior Angles of a Polygon

Triangles
Types of Triangles
Types of Triangles, Perimeter, Parts of a Circle
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

Polygons
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
Number of Diagonals in a Polygon, Number of Handshakes at a Party
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 1
Surface Area of Prisms, Surface Area of Cylinders, Surface Area of Pyramids
Surface Area 2
Surface Area of Cone, Surface Area of Sphere, Surface Area of Joined Solids

Volume of Solids
Volume 1
3-D Solid Properties, Volume of Prisms, Volume of Cylinders, Volume of Cones
Volume 2
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 1
Pythagorean Theorem Proofs, Square Root Operations, Using the Pythagorean Theorem to find a Missing Hypotenuse
Pythagorean Theorem 2
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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