High School Geometry Curriculum

Below are the skills needed, with links to resources to help with that skill. We also enourage 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
Definition of Radian
Unit Circle
☐ Convert between radian and degree measures
Degrees (Angles)
Radians
Unit Circle
☐ Define a Steradian and know its relationship to square degrees.
Steradian
High School Geometry | Geometry
☐ Solve problems using compound loci
Definition of Locus
Set of All Points
Hyperbola
Ellipse
Parabola
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).
Circle
Area of Circle, Triangle, Square, Rectangle, Parallelogram, Trapezium, Ellipse and Sector
Area Calculation Tool
Polygons
Area of Irregular Polygons
Regular Polygons - Properties
Double Hearts Ratio
Perimeter
Activity: Garden Area
☐ Determine the length of an arc of a circle, given its radius and the measure of its central angle
Circle Sector and Segment
Definition of Arc
Definition of Radian
Radians
☐ Construct a bisector of a given angle, using a straightedge and compass, and justify the construction
Definition of Contruction (Geometry)
Definition of Compass (Drawing)
Angle Bisector Construction
☐ Construct the perpendicular bisector of a given segment, using a straightedge and compass, and justify the construction
Definition of Contruction (Geometry)
Definition of Compass (Drawing)
Line Bisector Construction
☐ Construct lines parallel (or perpendicular) to a given line through a given point, using a straightedge and compass, and justify the construction
Definition of Contruction (Geometry)
Definition of Compass (Drawing)
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 Contruction (Geometry)
Definition of Compass (Drawing)
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
☐ Identify corresponding parts of congruent triangles
Congruent Triangles
☐ Investigate, justify, and apply the isosceles triangle theorem and its converse
Definition of Isosceles Triangle
Triangles - Equilateral, Isosceles and Scalene
☐ 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
☐ 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
Definition of Parallelogram
Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid, Parallelogram
☐ Investigate, justify, and apply theorems about special parallelograms (rectangles, rhombuses, squares) involving their angles, sides, and diagonals
Interactive Quadrilaterals
Definition of Rectangle
Definition of Rhombus
Definition of Square
Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid, Parallelogram
☐ Investigate, justify, and apply theorems about trapezoids (including isosceles trapezoids) involving their angles, sides, medians, and diagonals
Interactive Quadrilaterals
Definition of Trapezoid
Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid, Parallelogram
☐ Justify that some quadrilaterals are parallelograms, rhombuses, rectangles, squares, or trapezoids
Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid, Parallelogram
Interactive Quadrilaterals
☐ Investigate, justify, and apply theorems about geometric relationships based on the properties of the line segment joining the midpoints of two sides of a triangle
Theorems about Similar Triangles
☐ 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
☐ 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
☐ 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
Definition of Tangent (line)
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
Definition of Perpendicular
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
Definition of Similar
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
☐ Construct a circle touching three points using a straight edge and compass.
Circle touching 3 Points Construction
Circumscribe a Circle in a Triangle Construction
☐ Circumscribe a circle on a triangle using a straight edge and compass.
Circumscribe a Circle in 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.
Regular Polygons - Properties
☐ Know how to calculate the area of a regular polygon given the number of sides and the length of its apothem.
Regular Polygons - Properties
☐ Investigate, justify, and apply theorems about the number of diagonals of regular polygons.
Regular Polygons - Properties
☐ 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
How To Find if Triangles are 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.
Circle Theorems
Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid, Parallelogram
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
Definition of Cylinder
Activity: Soup Can
☐ 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
☐ 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
☐ 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
☐ 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 if two planes are perpendicular to the same line, they are parallel
Perpendicular and Parallel
☐ Understand what is meant by the cross section of a prism, cylinder or pyramid and recognize the shape of the cross section.
Cross Sections
Prisms with Examples
Pyramids
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
Spinning Octahedron
Spinning Icosahedron
Spinning Dodecahedron
Spinning Cube (Hexahedron)
Spinning Pentagonal Pyramid
Spinning Square Pyramid
Spinning Tetrahedron
Vertices, Edges and Faces
Activity: Investigating the Platonic Solids and other solids
☐ Understand why there are exactly five Platonic solids.
Platonic Solids - Why Five?
☐ Know the properties of a torus, including surface area = 4pi2Rr and volume is 2pi2Rr2
Torus
High School Geometry | Trigonometry
☐ Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the sides
Sohcahtoa: Sine, Cosine, Tangent
Sine, Cosine, Tangent
Finding an Angle in a Right Angled Triangle
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
Trigonometry
☐ 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
☐ Determine the measure of a third side of a right triangle using the Pythagorean theorem, given the lengths of any two sides
Pythagorean Theorem Proof
Pythagoras Theorem
Definition of Pythagoras Theorem
3, 4, 5 Triangle
Pythagorean Triples
Activity: A Walk in the Desert
Activity: Pythagoras' Theorem
Activity: Drawing Squares
☐ Express and apply the six trigonometric functions as ratios of the sides of a right triangle
Sohcahtoa: Sine, Cosine, Tangent
Definition of Sine
Definition of Cosine
Definition of Tangent (function)
Definition of Cosecant
Definition of Secant (function)
Definition of Cotangent
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
Unit Circle
☐ Know and apply the co-function and reciprocal relationships between trigonometric ratios
Trigonometry
Sine, Cosine, Tangent
Trigonometric Identities
Definition of Cotangent
Definition of Secant (function)
Definition of Cosecant
☐ 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)
Unit Circle
☐ 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
Inverse Functions
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)
Unit Circle
Sine, Cosine, Tangent
Sine, Cosine and Tangent in Four Quadrants
Cartesian Coordinates
Inverse Sine, Cosine, Tangent
☐ 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 or 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
☐ Determine the area of a triangle or a parallelogram, given the measure of two sides and the included angle
Area of Triangles Without Right Angles
☐ 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
☐ 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
☐ 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 Angle Triangles
Pythagorean Theorem Proof
Pythagoras Theorem
Definition of Pythagoras Theorem
Pythagorean Triples
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
Cartesian Coordinates
Sine, Cosine and Tangent in Four Quadrants

 

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