High School Geometry Curriculum

Below are skills needed, with links to resources to help with that skill. We also encourage plenty of exercises and book work. Curriculum Home

Important: this is a guide only.
Check with your local education authority to find out their requirements.

High School Geometry | Measurement
☐ Define radian measure
☐ Radians
☐ Radian Definition
☐ Convert between radian and degree measures
☐ Degrees
☐ Radians
☐ Define a Steradian and know its relationship to square degrees.
☐ Steradian
High School Geometry | Geometry (Plane)
☐ Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle Note: Figures may include triangles, rectangles, squares, parallelograms, rhombuses, trapezoids, circles, semi-circles, quarter-circles, and regular polygons (perimeter only).
☐ Polygons
☐ Circle
☐ Area of Circle Triangle Square Rectangle Parallelogram Trapezium Ellipse and Sector
☐ Area Calculator
☐ Double Hearts Ratio Puzzle
☐ Perimeter
☐ Activity: Garden Area
☐ Interactive Polygons
☐ Determine the length of an arc of a circle, given its radius and the measure of its central angle
☐ Circle Sector and Segment
☐ Arc Definition
☐ Radians
☐ Definition of Arc Length
☐ Construct a bisector of a given angle, using a straightedge and compass, and justify the construction
☐ Definition of Construction (Geometry)
☐ Definition of Compass
☐ Angle Bisector Construction
☐ Bisect
☐ Construct the perpendicular bisector of a given segment, using a straightedge and compass, and justify the construction
☐ Definition of Construction (Geometry)
☐ Definition of Compass
☐ Line Segment Bisector Construction
☐ Bisect
☐ Construct lines parallel (or perpendicular) to a given line through a given point, using a straightedge and compass, and justify the construction
☐ Definition of Construction (Geometry)
☐ Definition of Compass
☐ Parallel Line through a Point Construction
☐ Perpendicular to a Point on a Line Construction
☐ Perpendicular to a Point NOT on a Line Construction
☐ Construct an equilateral triangle, using a straightedge and compass, and justify the construction
☐ Definition of Construction (Geometry)
☐ Definition of Compass
☐ Equilateral Triangle OR 60 degree angle Construction
☐ Investigate and apply the concurrence of medians, altitudes, angle bisectors, and perpendicular bisectors of triangles
☐ Angle Bisector Construction
☐ Perpendicular to a Point on a Line Construction
☐ Bisect
☐ Triangle Centers
☐ Solve problems using compound loci
☐ Definition of Locus
☐ Set of All Points
☐ Identify corresponding parts of congruent triangles and other figures
☐ Congruent
☐ Congruent Triangles
☐ Investigate, justify, and apply the isosceles triangle theorem and its converse
☐ Definition of Isosceles Triangle
☐ Triangles - Equilateral Isosceles and Scalene
☐ Investigate, justify, and apply theorems about geometric inequalities, using the exterior angle theorem
☐ Triangles Contain 180 Degrees
☐ Exterior Angle
☐ Based on the measure of given pairs of angles formed by the transversal and the lines, determine whether two lines cut by a transversal are parallel.
☐ Alternate Exterior Angles
☐ Alternate Interior Angles
☐ Consecutive Interior Angles
☐ Corresponding Angles
☐ Parallel Lines and Pairs of Angles
☐ Transversals
☐ Investigate, justify, and apply theorems about the sum of the measures of the interior and exterior angles of polygons
☐ Exterior Angles of Polygons
☐ Interior Angles of Polygons
☐ Regular Polygons - Properties
☐ Polygons
☐ Interactive Polygons
☐ Investigate, justify, and apply theorems about each interior and exterior angle measure of regular polygons
☐ Exterior Angles of Polygons
☐ Interior Angles of Polygons
☐ Regular Polygons - Properties
☐ Polygons
☐ Investigate, justify, and apply theorems about parallelograms involving their angles, sides, and diagonals
☐ Interactive Quadrilaterals
☐ Parallelogram Definition
☐ Quadrilaterals - Square Rectangle Rhombus Trapezoid Parallelogram
☐ Parallelogram
☐ Investigate, justify, and apply theorems about special parallelograms (rectangles, rhombuses, squares) involving their angles, sides, and diagonals
☐ Interactive Quadrilaterals
☐ Definition of Rectangle
☐ Rhombus Definition
☐ Square Definition
☐ Quadrilaterals - Square Rectangle Rhombus Trapezoid Parallelogram
☐ Square
☐ Rectangle
☐ Rhombus
☐ Kite
☐ Investigate, justify, and apply theorems about trapezoids (including isosceles trapezoids) involving their angles, sides, medians, and diagonals
☐ Interactive Quadrilaterals
☐ Trapezoid Definition
☐ Quadrilaterals - Square Rectangle Rhombus Trapezoid Parallelogram
☐ Trapezoid
☐ Justify that some quadrilaterals are parallelograms, rhombuses, rectangles, squares, or trapezoids
☐ Quadrilaterals - Square Rectangle Rhombus Trapezoid Parallelogram
☐ Interactive Quadrilaterals
☐ Rectangle
☐ Rhombus
☐ Square
☐ Parallelogram
☐ Trapezoid
☐ Kite
☐ Investigate, justify, and apply theorems about similar triangles
☐ Similar Triangles
☐ Theorems about Similar Triangles
☐ Given one or more lines parallel to one side of a triangle and intersecting the other two sides of the triangle, investigate, justify, and apply theorems about proportional relationships among the segments of the sides of the triangle.
☐ Theorems about Similar Triangles
☐ Similar Triangles
☐ Investigate, justify, and apply theorems about mean proportionality: * the altitude to the hypotenuse of a right triangle is the mean proportional between the two segments along the hypotenuse * the altitude to the hypotenuse of a right triangle divides the hypotenuse so that either leg of the right triangle is the mean proportional between the hypotenuse and segment of the hypotenuse adjacent to that leg
☐ Mean Proportional and the Altitude and Leg Rules
☐ Investigate, justify, and apply theorems regarding chords of a circle: * perpendicular bisectors of chords * the relative lengths of chords as compared to their distance from the center of the circle
☐ Circle
☐ Definition of Chord
☐ Bisect
☐ Investigate, justify, and apply theorems about tangent lines to a circle: * a perpendicular to the tangent at the point of tangency * two tangents to a circle from the same external point * common tangents of two non-intersecting or tangent circles
☐ Tangent
☐ Point to Tangents on a Circle Construction
☐ Circle Theorems
☐ Investigate, justify, and apply theorems about the arcs determined by the rays of angles formed by two lines intersecting a circle when the vertex is: * inside the circle (two chords) * on the circle (tangent and chord) * outside the circle (two tangents, two secants, or tangent and secant)
☐ Circle Theorems
☐ Investigate, justify, and apply theorems regarding segments intersected by a circle: * along two tangents from the same external point * along two secants from the same external point * along a tangent and a secant from the same external point * along two intersecting chords of a given circle
☐ Circle Theorems
☐ Define, investigate, justify, and apply isometries in the plane (rotations, reflections, translations, glide reflections) Note: Use proper function notation.
☐ Reflection Symmetry
☐ Geometry Rotation
☐ Geometry - Reflection
☐ Point Symmetry
☐ Geometry Translation
☐ Rotational Symmetry
☐ Transformations
☐ Symmetry - Reflection and Rotation
☐ Investigate, justify, and apply the properties that remain invariant under translations, rotations, reflections, and glide reflections
☐ Geometry Rotation
☐ Transformations
☐ Symmetry - Reflection and Rotation
☐ Rotational Symmetry
☐ Geometry - Reflection
☐ Reflection Symmetry
☐ Point Symmetry
☐ Geometry Translation
☐ Justify geometric relationships (perpendicularity, parallelism, congruence) using transformational techniques (translations, rotations, reflections)
☐ Congruent
☐ Transformations
☐ Rotational Symmetry
☐ Perpendicular Definition
☐ Definition of Parallel
☐ Definition of Congruent
☐ Geometry Rotation
☐ Geometry Translation
☐ Define, investigate, justify, and apply similarities (dilations and the composition of dilations and isometries)
☐ Similar
☐ Similar Definition
☐ Geometry Resizing
☐ Transformations
☐ Investigate, justify, and apply the properties that remain invariant under similarities
☐ Similar
☐ Identify specific similarities by observing orientation, numbers of invariant points, and/or parallelism
☐ Similar
☐ Investigate, justify, and apply the analytical representations for translations, rotations about the origin of 90° and 180° reflections over the lines x=0, y=0, and y=x, and dilations centered at the origin
☐ Geometry - Reflection
☐ Geometry Rotation
☐ Transformations
☐ Geometry Translation
☐ Geometry Resizing
☐ Construct the center of a circle using a straight edge and compass.
☐ Center of Circle Construction
☐ Calculate the area of a segment of a circle, given the measure of a central angle and the radius of the circle
☐ Circle Sector and Segment
☐ Segment Definition
☐ Construct a circle touching three points using a straight edge and compass.
☐ Circle touching 3 Points Construction
☐ Circumscribe a Circle on a Triangle Construction
☐ Circumscribe a circle on a triangle using a straight edge and compass.
☐ Circumscribe a Circle on a Triangle Construction
☐ Circle touching 3 Points Construction
☐ Construct a triangle with three known sides using a ruler and compass, and justify the construction
☐ Constructing A Triangle With 3 Known Sides
☐ 3 4 5 Triangle
☐ Cut a line into n equal segments using a straightedge and compass, and justify the construction
☐ Cut a line into N segments Construction
☐ Construct a circle inscribed within a triangle (incircle) using a ruler and compass, and justify the construction.
☐ Angle Bisector Construction
☐ Inscribe a Circle in a Triangle Construction
☐ Construct a pentagon using a ruler and compass, and justify the construction.
☐ Pentagon Construction
☐ Construct a tangent from a point to a circle using a ruler and compass, and justify the construction.
☐ Point to Tangents on a Circle Construction
☐ Circle Theorems
☐ Know that the apothem of a regular polygon is the radius of its incircle, and know its relationship to the radius of the circumcircle of the polygon or the length of side of the polygon.
☐ Regular Polygons - Properties
☐ Apothem Definition
☐ Calculation of the area of a regular polygon from the number of sides and either the length of side, radius of the circumcircle or length of apothem.
☐ Regular Polygons - Properties
☐ Investigate, justify, and apply theorems about the number of diagonals of regular polygons.
☐ Regular Polygons - Properties
☐ Diagonals of Polygons
☐ Interactive Polygons
☐ Investigate the properties of the pentagram, and its relationship to the golden ratio.
☐ The Pentagram
☐ Use a ruler and drafting triangle to construct a line parallel to a given line and passing through a given point, or to construct a line perpendicular to a given line at a given point.
☐ Using a Ruler and Drafting Triangle
☐ Understand that a plane is a flat surface with no thickness that goes on forever.
☐ What is a Plane?
☐ Know how to find the ratio of the areas of similar shapes given the ratio of their lengths.
☐ Theorems about Similar Triangles
☐ Ratios
☐ Similar Triangles
☐ Similar
☐ Investigate and understand circle theorems incluing the Angle at the Center Theorem, the Angles Subtended by Same Arc Theorem and The Angle in the Semicircle Theorem.
☐ Circle
☐ Circle Theorems
☐ Investigate cyclic quadrilaterals and know that opposite angles of a cyclic quadrilateral are supplementary.
☐ Quadrilaterals - Square Rectangle Rhombus Trapezoid Parallelogram
☐ Circle Theorems
High School Geometry | Geometry (Solid)
☐ Use formulas to calculate volume and surface area of rectangular solids and cylinders
☐ Equations and Formulas
☐ Area of Circle Triangle Square Rectangle Parallelogram Trapezium Ellipse and Sector
☐ Spinning Cylinder
☐ Cuboids Rectangular Prisms and Cubes
☐ Volume of a Cuboid
☐ Volume Definition
☐ Activity: Soup Can
☐ Surface Area Definition
☐ Know and apply that if a line is perpendicular to each of two intersecting lines at their point of intersection, then the line is perpendicular to the plane determined by them
☐ Perpendicular and Parallel
☐ Parallel and Perpendicular Lines and Planes
☐ Know and apply that the lateral edges of a prism are congruent and parallel
☐ Cuboids Rectangular Prisms and Cubes
☐ Prisms with Examples
☐ Unfold the Prism Puzzle
☐ Know and apply that two prisms have equal volumes if their bases have equal areas and their altitudes are equal
☐ Volume of a Cuboid
☐ Cuboids Rectangular Prisms and Cubes
☐ Prisms with Examples
☐ Pouring Liquid
☐ Know and apply that the volume of a prism is the product of the area of the base and the altitude
☐ Volume of a Cuboid
☐ Cuboids Rectangular Prisms and Cubes
☐ Prisms with Examples
☐ Pouring Liquid
☐ Apply the properties of a regular pyramid, including: # lateral edges are congruent # lateral faces are congruent isosceles triangles # volume of a pyramid equals one-third the product of the area of the base and the altitude
☐ Spinning Pentagonal Pyramid
☐ Spinning Square Pyramid
☐ Spinning Tetrahedron
☐ Pyramids
☐ Spinning Triangular Pyramid
☐ Apply the properties of a cylinder, including: * bases are congruent * volume equals the product of the area of the base and the altitude * lateral area of a right circular cylinder equals the * product of an altitude and the circumference of the base
☐ Pouring Liquid
☐ Spinning Cylinder
☐ Apply the properties of a right circular cone, including: * lateral area equals one-half the product of the slant height and the circumference of its base * volume is one-third the product of the area of its base and its altitude
☐ Spinning Cone
☐ Apply the properties of a sphere, including: * the intersection of a plane and a sphere is a circle * a great circle is the largest circle that can be drawn on a sphere * two planes equidistant from the center of the sphere and intersecting the sphere do so in congruent circles * surface area is 4 pi r2 * volume is (4/3) pi r3
☐ Sphere
☐ Know and apply that through a given point there passes one and only one plane perpendicular to a given line
☐ Parallel and Perpendicular Lines and Planes
☐ Perpendicular and Parallel
☐ Know and apply that through a given point there passes one and only one line perpendicular to a given plane
☐ Parallel and Perpendicular Lines and Planes
☐ Perpendicular and Parallel
☐ Know and apply that two lines perpendicular to the same plane are coplanar
☐ Parallel and Perpendicular Lines and Planes
☐ Perpendicular and Parallel
☐ Know and apply that two planes are perpendicular to each other if and only if one plane contains a line perpendicular to the second plane
☐ Parallel and Perpendicular Lines and Planes
☐ Perpendicular and Parallel
☐ Know and apply that if a line is perpendicular to a plane, then any line perpendicular to the given line at its point of intersection with the given plane is in the given plane
☐ Parallel and Perpendicular Lines and Planes
☐ Perpendicular and Parallel
☐ Know and apply that if a line is perpendicular to a plane, then every plane containing the line is perpendicular to the given plane
☐ Parallel and Perpendicular Lines and Planes
☐ Perpendicular and Parallel
☐ Know and apply that if a plane intersects two parallel planes, then the intersection is two parallel lines
☐ Parallel and Perpendicular Lines and Planes
☐ Perpendicular and Parallel
☐ Know and apply that if two planes are perpendicular to the same line, they are parallel
☐ Perpendicular and Parallel
☐ Parallel and Perpendicular Lines and Planes
☐ Understand what is meant by the cross section of a prism, cylinder, pyramid, sphere or torus and recognize the shape of the cross section.
☐ Cross Sections
☐ Prisms with Examples
☐ Pyramids
☐ Torus
☐ Sphere
☐ Spinning Cylinder
☐ Understand what is meant by the dihedral angle between two planes.
☐ Dihedral Angle Calculator
☐ Understand Euler's Formula connecting the numbers of faces, vertices and edges of the Platonic solids and many other solids.
☐ Euler's Formula
☐ Platonic Solids
☐ Polyhedrons
☐ Vertices Edges and Faces
☐ Activity: Investigating Solids
☐ Understand why there are exactly five Platonic solids.
☐ Platonic Solids - Why Five?
☐ Know the properties of a torus, including the formulas for surface area and volume.
☐ Torus
☐ Use formulas to calculate the surface areas and volumes of the dodecahdron, the icosahedron, the octahedron and the tetrahedron
☐ Spinning Dodecahedron
☐ Spinning Icosahedron
☐ Spinning Octahedron
☐ Spinning Tetrahedron
☐ Spinning Cube
High School Geometry | Trigonometry
☐ Find the sine, cosine, and tangent ratios (or their reciprocals) of an angle of a right triangle, given the lengths of the sides
☐ Sohcahtoa: Sine Cosine Tangent
☐ Sine Cosine Tangent
☐ Trigonometry
☐ Determine the measure of an angle of a right triangle, given the length of any two sides of the triangle
☐ Sohcahtoa: Sine Cosine Tangent
☐ Finding an Angle in a Right Angled Triangle
☐ Random Trigonometry Questions
☐ Trigonometry
☐ Sine Cosine Tangent
☐ Find the measure of a side of a right triangle, given an acute angle and the length of another side
☐ Sohcahtoa: Sine Cosine Tangent
☐ Finding a Side in a Right-Angled Triangle
☐ Trigonometry
☐ Random Trigonometry Questions
☐ Sine Cosine Tangent
☐ Determine the measure of a third side of a right triangle using the Pythagorean theorem, given the lengths of any two sides
☐ Pythagoras Theorem
☐ Definition of Pythagoras Theorem
☐ 3 4 5 Triangle
☐ Activity: A Walk in the Desert
☐ Activity: Drawing Squares
☐ Activity: Pythagoras' Theorem
☐ Express and apply the six trigonometric functions as ratios of the sides of a right triangle, and know the trigonometric identities: tan(x) = sin(x)/cos(x) etc
☐ Sohcahtoa: Sine Cosine Tangent
☐ Sine Definition
☐ Cosine Definition
☐ Tangent
☐ Cosecant Definition
☐ Secant
☐ Cotangent Definition
☐ Trigonometry
☐ Sine Cosine Tangent
☐ Know the exact and approximate values of the sine, cosine, and tangent of 0°, 30°, 45°, 60°, 90°, 180°, and 270° angles
☐ Unit Circle
☐ Sine Cosine Tangent
☐ Sohcahtoa: Sine Cosine Tangent
☐ Solving Triangles by Reflection
☐ Sketch and use the reference angle for angles in standard position
☐ Sine Cosine and Tangent in Four Quadrants
☐ Unit Circle
☐ Know and apply the co-function and reciprocal relationships between trigonometric ratios
☐ Trigonometry
☐ Sine Cosine Tangent
☐ Trigonometric Identities
☐ Cotangent Definition
☐ Secant
☐ Cosecant Definition
☐ Magic Hexagon for Trig Identities
☐ Use the reciprocal and co-function relationships to find the values of the secant, cosecant, and cotangent of 0°, 30°, 45°, 60°, 90°, 180°, and 270° angles
☐ Unit Circle
☐ Trigonometric Identities
☐ Sketch the unit circle and represent angles in standard position
☐ Unit Circle
☐ Trigonometry
☐ Interactive Unit Circle
☐ Find the value of trigonometric functions, if given a point on the terminal side of angle (theta)
☐ Polar and Cartesian Coordinates
☐ Sine Cosine and Tangent in Four Quadrants
☐ Activity: A Walk in the Desert 2
☐ Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function
☐ Domain Range and Codomain
☐ Graphs of Sine Cosine and Tangent
☐ Inverse Functions
☐ Inverse Sine Cosine Tangent
☐ Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent
☐ Finding an Angle in a Right Angled Triangle
☐ Inverse Functions
☐ Inverse Sine Cosine Tangent
☐ Sketch the graphs of the inverses of the sine, cosine, and tangent functions
☐ Graphs of Sine Cosine and Tangent
☐ Equation Grapher
☐ Inverse Sine Cosine Tangent
☐ Determine the trigonometric functions of any angle, using technology
☐ Scientific Calculator
☐ Justify the Pythagorean identities
☐ Pythagoras Theorem
☐ Trigonometric Identities
☐ Unit Circle
☐ Solve simple trigonometric equations for all values of the variable from 0° to 360° (four quadrants)
☐ Sine Cosine and Tangent in Four Quadrants
☐ Inverse Sine Cosine Tangent
☐ Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function
☐ Graphs of Sine Cosine and Tangent
☐ Definition of Frequency
☐ Amplitude Period Phase Shift and Frequency
☐ Introduction to Waves
☐ Sketch and recognize one cycle of a function of the form y = A sin(Bx) or y = A cos(Bx)
☐ Function Grapher and Calculator
☐ Sketch and recognize the graphs of the functions y=sec(x), y=csc(x), y=tan(x), and y=cot(x)
☐ Graphs of Sine Cosine and Tangent
☐ Function Grapher and Calculator
☐ Write the trigonometric function that is represented by a given periodic graph
☐ Graphs of Sine Cosine and Tangent
☐ Solve for an unknown side or angle, using the Law of Sines
☐ Triangle Identities
☐ The Law of Sines
☐ Determine the area of a triangle or a parallelogram, given the measure of two sides and the included angle
☐ The Law of Sines
☐ Area of Triangles
☐ Determine the solution(s) of triangles from the SSA situation (ambiguous case)
☐ Solving SSA Triangles
☐ Apply the angle sum and difference formulas for trigonometric functions
☐ Trigonometric Identities
☐ Apply the double-angle and half-angle formulas for trigonometric functions
☐ Trigonometric Identities
☐ Determine the congruence of two triangles by using one of the five congruence techniques (SSS, SAS, ASA, AAS, HL), given sufficient information about the sides and/or angles of two congruent triangles
☐ Congruent Triangles
☐ How To Find if Triangles are Congruent
☐ Investigate, justify, and apply theorems about the sum of the measures of the angles of a triangle
☐ Triangles Contain 180 Degrees
☐ Interactive Triangles
☐ Triangles - Equilateral Isosceles and Scalene
☐ Investigate, justify, and apply the triangle inequality theorem
☐ Triangle Inequality Theorem Definition
☐ Determine either the longest side of a triangle given the three angle measures or the largest angle given the lengths of three sides of a triangle
☐ The Law of Cosines
☐ Solving SSS Triangles
☐ Investigate, justify, and apply theorems about the centroid of a triangle, dividing each median into segments whose lengths are in the ratio 2:1
☐ Centroid and Center of Gravity
☐ Triangle Centers
☐ Establish similarity of triangles, using the following theorems: AA, SAS, and SSS
☐ Similar Triangles
☐ How To Find if Triangles are Similar
☐ Investigate, justify, and apply the Pythagorean theorem and its converse
☐ Right-Angled Triangles
☐ Pythagorean Theorem Proof
☐ Pythagoras Theorem
☐ Definition of Pythagoras Theorem
☐ 3 4 5 Triangle
☐ Activity: A Walk in the Desert
☐ Sketch and recognize the graphs of the functions y=sin(x), y=cos(x) and y=tan(x)
☐ Graphs of Sine Cosine and Tangent
☐ Sine Function - Graph Exercise
☐ Trigonometry
☐ Find the area of a triangle given the lengths of its three sides, using Heron's formula.
☐ Heron's Formula
☐ Recognize that an AAA triangle is impossible to solve.
☐ Solving AAA Triangles
☐ Use the symmetric properties of an equilateral triangle to solve triangles by reflection.
☐ Solving Triangles by Reflection
☐ Be familiar with the triangle identities that are true for all triangles: The Law of Sines, The Law of Cosines and the Law of Tangents.
☐ Triangle Identities
☐ The Law of Sines
☐ The Law of Cosines
☐ Know and apply the opposite angle identities: sin(-A) = -sin(A), cos(-A) = cos(A) and tan(-A) = -tan(A)
☐ Trigonometric Identities
☐ Know how to find the values of sine, cosine and tangent in each of the four quadrants; including determining the correct sign.
☐ Sine Cosine Tangent
☐ Sine Cosine and Tangent in Four Quadrants
☐ Unit Circle
☐ Solve for an unknown side or angle, using the Law of Cosines
☐ Triangle Identities
☐ The Law of Cosines
☐ Solve a triangle using the Law of Sines and the Law of Cosines
☐ Triangle Identities
☐ The Law of Cosines
☐ The Law of Sines
☐ Solving Triangles
☐ Solving AAS Triangles
☐ Solving ASA Triangles
☐ Solving SAS Triangles
☐ Solving SSA Triangles
☐ Solving SSS Triangles
☐ Solving AAA Triangles
☐ Use the magic hexagon to remember trigonometric identities
☐ Magic Hexagon for Trig Identities
☐ Trigonometric Identities