Geometry – Credit Recovery
Course details
Duration
10 weeks or less
Lectures
89
Video
During Intros
Level
Beginner
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Our online Geometry course builds upon students’ command of geometric relationships and formulating mathematical arguments. Students learn through discovery and application, developing the skills they need to break down complex challenges and demonstrate their knowledge in new situations.
Course topics include reasoning, proof, and the creation of sound mathematical arguments; points, lines, and angles; triangles and trigonometry; quadrilaterals and other polygons; circles; congruence, similarity, transformations, and constructions; coordinate geometry; three-dimensional solids; and applications of probability.
This course supports all students as they develop computational fluency and deepen conceptual understanding. Students begin each lesson by discovering new concepts through guided instruction, and then confirm their understanding in an interactive, feedback-rich environment. Modeling activities equip students with tools for analyzing a variety of real-world scenarios and mathematical ideas. Journaling activities allow students to reason abstractly and quantitatively, construct arguments, critique reasoning, and communicate precisely. Performance tasks prepare students to synthesize their knowledge in novel, real-world scenarios and require that they make sense of multifaceted problems and persevere in solving them.
Unit 1: Foundations of Geometry
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Lesson 1: Induction: The Search for Rules and Patterns- Study - Induction: The Search for Rules and Patterns: Learn about looking for patterns, making conjectures, cross-referencing to history and science, real-world examples of inductive reasoning, building a triangle, and examples of symmetry.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Induction: The Search for Rules and Patterns: Take a quiz to check your understanding of what you have learned.
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Lesson 2: Deduction: Making A Case
- Study - Deduction: Making a Case: Learn about the definition of deductive reasoning; postulates and conditional statements; and using deductive reasoning in proofs. Explore a real-world example of deducing that deals with the combination of a lock.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Deduction: Making a Case: Take a quiz to check your understanding of what you have learned.
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Lesson 3: The Look and Language of Logic
- Study - The Look and Language of Logic: Explore examples of geometric reasoning. Learn about converses, inverses, and contrapositives of conditional statements.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - The Look and Language of Logic: Take a quiz to check your understanding of what you have learned.
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Lesson 4: Introduction to Proofs
- Study - Introduction to Proofs: Learn about postulates and axioms, givens, proof by contradiction (indirect proof), theorems and corollaries, and the axiomatic method.
- Quiz - Introduction to Proofs: Take a quiz to check your understanding of what you have learned.
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Lesson 5: Basic Postulates in Geometry
- Study - Basic Postulates in Geometry: Learn about the relationship of rays, lines, and angles to direction; the definition of a line; notation for rays and lines; building and defining an angle (including its vertex and sides); conventions for naming angles; and straight and zero angles.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Basic Postulates in Geometry: Take a quiz to check your understanding of what you have learned.
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Lesson 6: Planes and the Space of Geometry
- Study - Planes and the Space of Geometry: Learn about dimensionality, collinear points, two-dimensional objects, the geometric plane, the flat plane, postulate coplanar objects, and three-dimensional objects (solids).
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Planes and the Space of Geometry: Take a quiz to check your understanding of what you have learned.
- Practice - Modeling: Logo Design: Use your knowledge of location, direction, and angles to model and solve a real-world problem.
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Lesson 7: Intersecting Lines and Proofs
- Study - Intersecting Lines and Proofs: Learn about intersections that form vertical angles; the vertical angle theorem; perpendicular lines, rays, and segments; distance and length; and perpendicular bisectors.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Intersecting Lines and Proofs: Take a quiz to check your understanding of what you have learned.
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Lesson 8: Parallel Lines and Proofs
- Study - Parallel Lines and Proofs: Learn about skew lines, coplanar lines that do not intersect, parallel line notation, transversals and corresponding angles, alternate interior angles, consecutive interior angles, and parallel line theorems.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Parallel Lines and Proofs: Take a quiz to check your understanding of what you have learned.
- Journal - Consecutive Angle Theorem: Use what you know about lines and angles to critique the reasoning of others and prove a theorem.
- Study - Solving the Mirror Problem: Learn about applying theorems from this unit to the problem of measuring light reflected off a mirror. Learn about the law of reflection.
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Lesson 9: Foundations of Geometry Wrap-Up
- Checkup - Foundations of Geometry Practice Problems: Check your understanding of the topics in this unit.
- Review - Foundations of Geometry: Get ready for the unit test by reviewing important ideas and skills.
- Test (CS) - Foundations of Geometry: Take a computer-scored test to check what you have learned in this unit.
- Test (T S) - Foundations of Geometry: Take a teacher-scored test to check what you have learned in this unit.
Unit 2: Triangles
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Lesson 1: What Is a Triangle?
- Study - What Is a Triangle? Learn about the definition and parts of a triangle; opposite and included figures; naming and sorting triangles; equilateral, isosceles, and scalene triangles; and the triangle inequality theorem.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Naming Triangles by Angle Measures: Take a quiz to check your understanding of what you have learned.
- Quiz - Naming Triangles by Side Lengths: Take a quiz to check your understanding of what you have learned.
- Quiz - The Triangle Inequality Theorem: Take a quiz to check your understanding of what you have learned.
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Lesson 2: The Angles of a Triangle
- Study - The Angles of a Triangle: Explore the angle sum theorem and third angle theorem for triangles. Investigate the relationship between a given triangle's vertex and its exterior and remote interior angles.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Angle Theorems: Take a quiz to check your understanding of what you have learned.
- Quiz - Exterior and Remote Interior Angles: Take a quiz to check your understanding of what you have learned.
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Lesson 3: Congruence
- Study - Congruence: Learn about congruence, transformations of triangles, corresponding triangles, notation for writing congruence statements, and the CPCTC triangle congruence theorem.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Congruent Triangles: Take a quiz to check your understanding of what you have learned.
- Quiz - Properties of Congruence: Take a quiz to check your understanding of what you have learned.
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Lesson 4: Congruence Postulates
- Study - Congruence Postulates: Learn about postulates including the SSS, SAS, ASA, and AAS theorems.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Using Congruence Postulates: Take a quiz to check your understanding of what you have learned.
- Quiz - The AAS Theorem: Take a quiz to check your understanding of what you have learned.
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Lesson 5: Proofs of Congruence
- Study - Proofs of Congruence: Learn about proving that parts of triangles are congruent by using Thales's method for measuring the distance from ship to shore.
- Quiz - Proofs of Congruence: Take a quiz to check your understanding of what you have learned.
- Journal - Proofs of Congruence: Use what you know about congruence of triangles to prove the Perpendicular Bisector Theorem.
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Lesson 6: Similar Triangles
- Study - Similar Triangles: Learn about similarity versus congruence, testing for similarity among triangles, proportionality, the definition of similar triangles, and scale factor.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Similar Triangles: Take a quiz to check your understanding of what you have learned.
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Lesson 7: Similarity Theorems and Proportional Reasoning
- Study - Similarity Theorems and Proportional Reasoning: Learn about the ASA similarity postulate, the SSS similarity theorem, and the SAS similarity theorem.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Similarity Theorems: Take a quiz to check your understanding of what you have learned.
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Lesson 8: Triangle Theorems
- Study - Triangle Theorems: Learn and prove the isosceles triangle theorem and its converse. Investigate two corollaries involving angle measures for equilateral triangles. Explore theorems for scalene triangles. Apply what you have learned to solve Thales's problem.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Isosceles and Equilateral Triangles: Take a quiz to check your understanding of what you have learned.
- Quiz - Scalene Triangles: Take a quiz to check your understanding of what you have learned.
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Lesson 9: Medians and Altitudes
- Study - Medians and Altitudes: Identify and explore medians and altitudes. Discover their relationship to centroids, orthocenters, incenters, and circumcenters.
- Quiz - Medians and Altitudes: Take a quiz to check your understanding of what you have learned.
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Lesson 10: Bisectors and Midsegments
- Study - Bisectors and Midsegments: Identify and explore angle bisectors, perpendicular bisectors, and midpoint bisectors, and lines parallel to one side of a triangle to discover their relationships to circumcenters, incenters, and side lengths.
- Quiz - Bisectors and Midsegments: Take a quiz to check your understanding of what you have learned.
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Lesson 11: Performance Task: The Parallax Problem
- Study - The Parallax Problem: Learn to apply the concepts of congruence, similarity, ratio, and proportion to the solution of a real-world parallax problem.
- Project - Performance Task: The Parallax Problem: Apply the concepts of congruence, similarity, ratio, and proportion to solve a real-world problem.
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Lesson 12: Triangles Wrap-Up
- Checkup - Triangles Practice Problems: Check your understanding of the topics in this unit.
- Review - Triangles: Get ready for the unit test by reviewing important ideas and skills.
- Test (CS) - Triangles: Take a computer-scored test to check what you have learned in this unit.
- Test (TS) - Triangles: Take a teacher-scored test to check what you have learned in this unit.
Unit 3: Right Triangles
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Lesson 1: The Pythagorean Theorem
- Study - The Pythagorean Theorem: Learn how the Pythagorean theorem applies only to right triangles and discover one proof of it. Learn about the converse of the Pythagorean theorem, Pythagorean triples, and applying the theorem to the problem of fitting a baseball bat into a rectangular trunk.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - The Pythagorean Theorem: Take a quiz to check your understanding of what you have learned.
- Journal - Proving the Pythagorean Theorem: Use what you know about congruence of triangles to prove the Pythagorean Theorem.
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Lesson 2: Congruent Right Triangles
- Study - Congruent Right Triangles: Learn about the HL, LL, HA, LA, and perpendicular bisector theorems. Learn about the angle bisector theorem and its converse.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Proving Right Triangle Congruence: Take a quiz to check your understanding of what you have learned.
- Quiz - Right Triangle Measurements: Take a quiz to check your understanding of what you have learned.
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Lesson 3: Similar Right Triangles
- Study - Similar Right Triangles: Explore the properties of similar right triangles. Prove that if an altitude is drawn from the right-angle vertex of a right triangle to its hypotenuse, then three similar triangles are formed. Calculate the missing sides of similar right triangles by using proportions and apply concepts learned to a miniature-golf problem.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Similar Right Triangles: Take a quiz to check your understanding of what you have learned.
- Practice - Modeling: The Pool Table Problem: Use your knowledge of similar right triangles to model a pool table and hit your ball in the pocket.
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Lesson 4: Special Right Triangles
- Study - Special Right Triangles: Explore 45-45-90 and 30-60-90 triangles as special cases of right triangles and learn how to apply the ratios of their side lengths.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - 45-45-90 Right Triangles: Take a quiz to check your understanding of what you have learned.
- Quiz - 30-60-90 Right Triangles: Take a quiz to check your understanding of what you have learned.
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Lesson 5: Right Triangles Wrap-Up
- Checkup - Right Triangles Practice Problems: Check your understanding of the topics in this unit.
- Review - Right Triangles: Get ready for the unit test by reviewing important ideas and skills.
- Test (CS) - Right Triangles: Take a computer-scored test to check what you have learned in this unit.
- Test (TS) - Right Triangles: Take a teacher-scored test to assess what you have learned in this unit.
Unit 4: Trigonometry
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Lesson 1: Trigonometric Ratios
- Study - Trigonometric Ratios: Learn the definitions of sine, cosine, and tangent. Memorize the shortcut "soh-cah-toa" as a way to relate these ratios. Explore the use of trigonometric ratios in the solution of a real-world problem involving the construction of a cable car.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Trigonometric Ratios: Take a quiz to check your understanding of what you have learned.
- Practice - Modeling: Leaning Towers: Use your knowledge of right triangles, trigonometric ratios, and the Pythagorean Theorem to model and solve a real-world problem.
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Lesson 2: Law of Cosines and Proofs
- Study - Law of Cosines and Proofs: Use the law of cosines to solve triangles.
- Checkup - Practice Problems: Complete a set of practice problems using the law of cosines.
- Quiz - Law of Cosines and Proofs: Take a quiz to assess your understanding of the material.
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Lesson 3: Law of Sines and Proofs
- Study - Law of Sines and Proofs: Use the law of sines to solve triangles and to explore the ambiguous case.
- Checkup - Practice Problems: Complete a set of practice problems using the law of sines.
- Journal - Law of Sines and Proofs: Use what you know about triangles and trigonometric ratios to prove the law of sines.
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Lesson 4: Trigonometry Wrap-Up
- Checkup - Trigonometry Practice Problems: Check your understanding of the topics in this unit.
- Review - Trigonometry: Prepare for the unit test by reviewing key concepts and skills.
- Test (CS) - Trigonometry: Take a computer-scored test to assess what you have learned in this unit.
- Test (TS) - Trigonometry: Take a teacher-scored test to assess what you have learned in this unit.
Unit 5: Quadrilaterals and Other Polygons
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Lesson 1: Angle Sums of a Polygon and Proofs
- Study: - Angle Sums of a Polygon and Proofs: Learn about the diagonal of a polygon, the formula for the sum of the measures of a polygon's interior angles and exterior angles, and a theorem for the sum of their measures.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Angle Sums of a Polygon and Proofs: Take a quiz to check your understanding of what you have learned.
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Lesson 2: Parallelograms and Proofs
- Study - Parallelograms and Proofs: Learn about the definition of a parallelogram, properties and theorems of parallelograms, consecutive angle pairs, and diagonals.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Parallelograms and Proofs: Take a quiz to check your understanding of what you have learned.
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Lesson 3: Tests for Parallelograms
- Study - Tests for Parallelograms: Explore parallelogram theorems involving opposite side lengths, opposite and consecutive angle measures, and bisecting diagonals. Then work through a sample proof.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Tests for Parallelograms: Take a quiz to check your understanding of what you have learned.
- Practice - Modeling: Finding Parallelograms: Use your knowledge of quadrilaterals to model and solve a real-world problem.
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Lesson 4: Rectangles
- Study - Rectangles: Learn about the definition of a rectangle, congruent diagonal theorems, and right angle theorems. Explore a sample problem about using the congruent diagonal theorem to prove that a window is rectangular.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Rectangles: Take a quiz to check your understanding of what you have learned.
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Lesson 5: Rhombi and Squares
- Study - Rhombi and Squares: Identify the properties and definitions of a rhombus and a square. Prove that the diagonals of a rhombus are perpendicular. Investigate how diagonals of a rhombus bisect opposite vertices. Apply the properties of rhombi and squares to find missing side lengths, diagonal lengths, and angle measures.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Rhombi and Squares: Take a quiz to check your understanding of what you have learned.
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Lesson 6: Trapezoids
- Study - Trapezoids: Learn the definition of a trapezoid and identify its parts. Explore how base angles and diagonals of an isosceles trapezoid are congruent. Investigate the medians of a trapezoid. Apply the properties of trapezoids and isosceles trapezoids to find missing side lengths and median lengths.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Trapezoids: Take a quiz to check your understanding of what you have learned.
- Journal - The Stone Arch: Use what you know about triangles and parallelograms to solve a real-world problem.
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Lesson 7: Quadrilaterals and Other Polygons Wrap-Up
- Checkup - Quadrilaterals and Other Polygons Practice Problems: Check your understanding of the topics in this unit.
- Review - Quadrilaterals and Other Polygons: Get ready for the unit test by reviewing important ideas and skills.
- Test (CS) - Quadrilaterals and Other Polygons: Take a computer-scored test to check what you have learned in this unit.
- Test (TS) - Quadrilaterals and Other Polygons: Take a teacher-scored test to check what you have learned in this unit.
Unit 6: Circles Without Coordinates
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Lesson 1: What Is a Circle?
- Study - What Is a Circle? Learn about the definition of a circle and about its center, radius, and circumference.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - What Is a Circle? Take a quiz to check your understanding of what you have learned.
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Lesson 2: Chords
- Study - Chords: Investigate the properties and definitions of chords and diameters. Discover that two chords are congruent if they are the same distance from the center of the circle. Prove that the radius bisects a chord if it is perpendicular to the chord.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Congruent Chords: Take a quiz to check your understanding of what you have learned.
- Quiz - Chords and Perpendicular Radii: Take a quiz to check your understanding of what you have learned.
- Quiz - Diameter of a Circle: Take a quiz to check your understanding of what you have learned.
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Lesson 3: Arcs
- Study - Arcs: Learn the definitions of arc, endpoint, central angle, and intercept. Learn about minor and major arcs and semicircles, arc notation, the measure of minor and major arcs, and the arc congruence and congruent chord theorems.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Arc Types and Measure: Take a quiz to check your understanding of what you have learned.
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Lesson 4: Chord and Arc Relationships
- Study - Chord and Arc Relationships: Learn the definitions of arc, endpoint, central angle, and intercept. Learn about minor and major arcs and semicircles, arc notation, the measure of minor and major arcs, and the arc congruence and congruent chord theorems.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Congruent Chords and Circle Angle Measure: Take a quiz to check your understanding of what you have learned.
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Lesson 5: Circles, Angles, and Proofs
- Study - Circles, Angles, and Proofs: Learn the definition of an inscribed angle. Experiment with inscribed angles and their intercepted arcs. Discover and prove that an inscribed angle is half the measure of its intercepted arc. Discover and prove the intersecting chord theorem.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Inscribed Angles: Take a quiz to check your understanding of what you have learned.
- Quiz - Intersecting Chord Theorem: Take a quiz to check your understanding of what you have learned.
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Lesson 6: Secants, Tangents, and Proofs
- Study - Secants, Tangents, and Proofs: Learn about the definition of secant and about secant-secant angle, its theorem, and proving the theorem. Learn about tangent line, point of tangency and tangent segments, tangents perpendicular to a circle's radius, a tangent-tangent angle and its theorem, and a tangent-chord angle and its theorem. Explore a sample proof.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Secant-Secant Angles: Take a quiz to check your understanding of what you have learned.
- Quiz - Tangent-Chord Angles: Take a quiz to check your understanding of what you have learned.
- Quiz - Tangent-Tangent Angles and Their Intercepted Arcs: Take a quiz to check your understanding of what you have learned.
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Lesson 7: Circumference and Arc Length
- Study - Circumference and Arc Length: Learn about the irrational number pi and the formula for finding the circumference of a circle. Apply circumference to a real-world problem about how to build a bridge that's tall enough for boats to travel beneath it. Learn about the degree measure of an arc and arc length. Derive the formula for arc length.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Circumference of a Circle: Take a quiz to check your understanding of what you have learned.
- Quiz - Arc Length: Take a quiz to check your understanding of what you have learned.
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Lesson 8: Area and Sectors
- Study - Area and Sectors: Learn about the formula for the area of a circle. Explore a case study comparing the cost per square inch of small and large pizzas. Learn about sectors and the area of a sector.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Area of a Circle: Take a quiz to check your understanding of what you have learned.
- Quiz - Area of a Sector: Take a quiz to check your understanding of what you have learned.
- Practice - Modeling: Stained Glass Window: Use what you know about finding the area of circles and sectors to model and solve a real-world problem.
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Lesson 9: Circles and Triangles
- Study - Circles and Triangles: Learn about inscribed objects; circumscribed objects; and the definitions of incenter and circumcenter.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Circles and Triangles: Take a quiz to check your understanding of what you have learned.
- Journal - Similar Circles: A peer uses dilation to prove that two circles are similar. Now you prove it using inscribed triangles.
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Lesson 10: Circles and Polygons
- Study - Circles and Polygons: Learn about the theorems of a quadrilateral inscribed in a circle and of a parallelogram inscribed in a circle.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Circles and Polygons: Take a quiz to check your understanding of what you have learned.
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Lesson 11: Circles Without Coordinates Wrap-Up
- Checkup - Circles Without Coordinates Practice Problems: Check your understanding of the topics in this unit.
- Review - Circles Without Coordinates: Get ready for the unit test by reviewing important ideas and skills.
- Test (CS) - Circles Without Coordinates: Take a computer-scored test to check what you have learned in this unit.
- Test (TS) - Circles Without Coordinates: Take a teacher-scored test to check what you have learned in this unit.
Unit 8: Coordinate Geometry
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Lesson 1: Midpoint Formula
- Study - Midpoint Formula: Learn about the midpoints of horizontal, vertical, and diagonal line segments and about the midpoint formula. Complete a sample problem.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Midpoint Formula: Take a quiz to check your understanding of what you have learned.
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Lesson 2: The Distance Formula
- Study - The Distance Formula: Derive the distance formula from the Pythagorean theorem. Use this formula to calculate the distance between any two points. Apply the distance formula in a real-world problem that involves locating the shortest route on a nautical map.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - The Distance Formula: Take a quiz to check your understanding of what you have learned.
- Journal - The Distance Formula: Use what you know about the midpoint and distance formulas to critique the reasoning of others.
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Lesson 3: Patterns and Lines
- Study - Patterns and Lines: Learn about linear equations, ordered pairs, and data points that form a straight line.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Patterns and Lines: Take a quiz to check your understanding of what you have learned.
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Lesson 4: Slope
- Study - Slope: Learn about measuring slope, rise, and run; the slope formula; negative zero and undefined slope; and measuring the rate of change of a dependent variable.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Computing Slope: Take a quiz to check your understanding of what you have learned.
- Practice - Modeling: The Rescue Ship: Use your knowledge of parallel lines and the slope formula to steer a ship through dangerous waters.
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Lesson 5: Equations of Lines
- Study - Equations of Lines: Learn about and explore examples of properties of lines, the y-intercept, the slope-intercept equation, and the point slope equation.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Equations of Lines — Part I: Take a quiz to check your understanding of what you have learned.
- Quiz - Equations of Lines — Part II: Take a quiz to check your understanding of what you have learned.
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Lesson 6: Equations of Parallel and Perpendicular Lines and Proofs
- Study - Equations of Parallel and Perpendicular Lines and Proofs: Learn about the definitions and slopes of parallel and perpendicular lines. Learn about negative reciprocals.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Equations of Parallel and Perpendicular Lines and Proofs: Take a quiz to check your understanding of what you have learned.
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Lesson 7: Coordinate Geometry with Polygons
- Study - Coordinate Geometry with Polygons: Investigate the properties of polygons using coordinate geometry and congruence transformations on the coordinate plane.
- Checkup - Practice Problems: Complete a set of practice problems to hone your calculation skills.
- Quiz - Coordinate Geometry with Polygons: Take a quiz to assess your understanding of the material.
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Lesson 8: Area of a Triangle with Coordinate Geometry
- Study - Area of a Triangle with Coordinate Geometry: Learn about the area of a polygon, square units, and the triangle area formula and theorem.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Area of a Triangle: Take a quiz to check your understanding of what you have learned.
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Lesson 9: Area and Perimeter of Polygons with Coordinate Geometry
- Study - Area and Perimeter of Polygons with Coordinate Geometry: Find the perimeter of any polygon. Determine the areas of irregular polygons by breaking them up into quadrilaterals and regular polygons. Use the apothem formula to find the area of a regular polygon. Complete sample problems about the area of irregular polygons.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Area and Perimeter of Polygons: Take a quiz to check your understanding of what you have learned.
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Lesson 10: Coordinate Geometry Wrap-Up
- Checkup - Practice Problems: Check your understanding of the topics in this unit.
- Review - Coordinate Geometry: Get ready for the unit test by reviewing important ideas and skills.
- Test (CS) - Coordinate Geometry: Take a computer-scored test to check what you have learned in this unit.
- Test (TS) - Coordinate Geometry: Take a teacher-scored test to check what you have learned in this unit.
Unit 9: Conic Sections
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Lesson 1: From Lines to Conic Sections
- Study - From Lines to Conic Sections: Learn about four kinds of conic sections, as well as the definitions of right circular cone, nappe, vertex, conic section, and cross section.
- Checkup - Practice Problems: Complete a set of practice problems to check your understanding of the lesson.
- Quiz - Linear Equations: Take a quiz to check your understanding of what you have learned.
- Quiz - What Is a Conic Section? Take a quiz to check your understanding of what you have learned.
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Lesson 2: Geometry of Conic Sections
- Study - Geometry of Conic Sections: Learn about parts and geometric properties of circles, ellipses, hyperbolas, and parabolas.
- Checkup - Practice Problems: Complete a set of practice problems to check your understanding of the lesson.
- Quiz - Geometry of Circles and Ellipses: Take a quiz to check your understanding of what you have learned.
- Quiz - Geometry of Hyperbolas and Parabolas: Take a quiz to check your understanding of what you have learned.
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Lesson 3: Circles with Coordinates and Proofs
- Study - Circles with Coordinates and Proofs: Use algebra to find an equation whose solution set is a circle. Learn about the standard equation for circles that are not centered at the origin.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Circles Centered at the Origin: Take a quiz to check your understanding of what you have learned.
- Quiz - Circles Not Centered at the Origin: Take a quiz to check your understanding of what you have learned.
- Journal - Point on a Circle: Use what you know about equations of circles to prove whether or not a point is on a circle.
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Lesson 4: Parabolas
- Study - Parabolas: Learn about finding a parabola's equation from its graph; the effect of the squared variable's coefficient on the parabola's orientation and shape; equations of parabolas with vertices at points other than the origin; vertex form and standard form of an equation for a parabola; and converting between vertex form and standard form.
- Checkup - Practice Problems: Complete a set of practice problems to check your understanding of the lesson.
- Quiz - Parabolas with Vertices at the Origin: Take a quiz to check your understanding of what you have learned.
- Quiz - Parabolas with Vertices Not at the Origin: Take a quiz to check your understanding of what you have learned.
- Quiz - Converting Parabolic Equations: Take a quiz to check your understanding of what you have learned.
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Lesson 5: Locus of Points
- Study - Locus of Points: Learn about defining objects in terms of points and given distances. Explore examples of a parabola and bisecting angles.
- Quiz - Locus of Points: Take a quiz to check your understanding of what you have learned.
- Practice - Modeling: Wildlife Sanctuary: Use what you know about locus of points to solve a real-world problem.
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Lesson 6: Conic Sections Wrap-Up
- Checkup - Conic Sections Practice Problems: Check your understanding of the topics in this unit.
- Review - Conic Sections: Get ready for the unit test by reviewing important ideas and skills.
- Test (CS) - Conic Sections: Take a computer-scored test to check what you have learned in this unit.
- Test (TS) - Conic Sections: Take a teacher-scored test to check what you have learned in this unit.
Unit 10: Constructions and Transformations
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Lesson 1: Constructions
- Study - Constructions: Learn about using a straightedge and a compass, common notions of Euclidean geometry, five postulates, constructing an equilateral triangle and a regular hexagon, bisecting an angle, and constructing a perpendicular bisector.
- Quiz - Constructions: Take a quiz to check your understanding of what you have learned.
- Practice - Modeling: Constructing a Square: Use your geometry skills to construct a square using only a straightedge and a compass.
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Lesson 2: Paper Folding
- Study - Paper Folding: Learn about constructing geometric solids with folding paper, coinciding objects bisecting an angle, and constructing a parallel line segment.
- Quiz - Paper Folding: Take a quiz to check your understanding of what you have learned.
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Lesson 3: Impossible Problems from Antiquity
- Study - Impossible Problems from Antiquity: Learn about the Delian problem (doubling a cube) and trisecting an angle.
- Quiz - Impossible Problems from Antiquity: Take a quiz to check your understanding of what you have learned.
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Lesson 4: Transformations
- Study - Transformations: Learn about rigid motions, describe the image and preimage, predict the results of transformations, and use a series of transformations to move figures onto themselves.
- Quiz - Transformations: Take a quiz to check your understanding of what you have learned.
- Journal - Transformations: Critique a conjecture about a series of transformations.
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Lesson 5: Symmetry
- Study - Symmetry: Learn about reflectional symmetry and line of symmetry and explore an example of an isosceles triangle. Learn about rotational symmetry, point of symmetry, and the symmetry of a human face.
- Quiz - Symmetry: Take a quiz to check your understanding of what you have learned.
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Lesson 6: Tessellations
- Study - Tessellations: Learn the definition and explore examples of tessellations. Discover the chessboard as an example of a regular tessellation. Learn about semiregular tessellations.
- Quiz - Tessellations: Take a quiz to check your understanding of what you have learned.
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Lesson 7: Constructions and Transformations Wrap-Up
- Checkup - Constructions and Transformations Practice Problems: Check your understanding of the topics in this unit.
- Review - Constructions and Transformations: Get ready for the unit test by reviewing important ideas and skills.
- Test (CS) - Constructions and Transformations: Take a computer-scored test to check what you have learned in this unit.
- Test (TS) - Constructions and Transformations: Take a teacher-scored test to check what you have learned in this unit.
Unit 11: Three-Dimensional Solids
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Lesson 1: Three Dimensions
- Study - Three Dimensions: Learn about measuring three-dimensional figures.
- Quiz - Three Dimensions: Take a quiz to check your understanding of what you have learned.
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Lesson 2: What Is a Polyhedron?
- Study - What Is a Polyhedron? Learn about the definition and elements of a polyhedron, prisms and their components, triangular and rectangular prisms, cubes, and regular and irregular pyramids.
- Quiz - What Is a Polyhedron? Take a quiz to check your understanding of what you have learned.
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Lesson 3: Cylinders and Cones
- Study - Cylinders and Cones: Learn about the definition, components, and properties of a cylinder; the definition and components of a cone; and the similarities between cones and pyramids.
- Quiz - Cylinders and Cones: Take a quiz to check your understanding of what you have learned.
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Lesson 4: Platonic Solids
- Study - Platonic Solids: Learn about polygonal numbers, regularity of Platonic solids, and building your own Platonic solids.
- Quiz - Platonic Solids: Take a quiz to check your understanding of what you have learned.
- Practice - Modeling: Solids: Practice with a real-world solid modeling application.
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Lesson 5: Surface Area
- Study - Surface Area: Learn about perimeter and surface area; base and lateral area; slant height versus altitude; and the formulas for surface area of a right prism, an oblique prism, a regular pyramid, an oblique cylinder, a right cone, and an oblique cone. Explore sample problems dealing with these subjects.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Surface Area of Regular Prisms and Pyramids: Take a quiz to check your understanding of what you have learned.
- Quiz - Surface Area of Right Cylinders and Cones: Take a quiz to check your understanding of what you have learned.
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Lesson 6: Volume
- Study - Volume: Learn about area and volume, the formulas for volume of a cube and a rectangular prism, and Bonaventura Francesco Cavalieri's principle. Learn about the formulas for volume of a cylinder, a pyramid, and a cone; explore sample problems dealing with these formulas. Learn about cross-sectional area.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Volume of Prisms, Cylinders, and Cubes: Take a quiz to check your understanding of what you have learned.
- Quiz - Volume of Cones, Cylinders, and Pyramids: Take a quiz to check your understanding of what you have learned.
- Journal - Volume: Think about and discuss how changing one dimension of a given shape changes its volume and surface area.
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Lesson 7: Spheres
- Study - Spheres: Learn about the definition of a sphere; the formulas for surface area and volume of a sphere; comparing the surface area and volume of a sphere, cube, cylinder, and cone; and using Cavalieri's principle to derive the formula for volume of a sphere.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Spheres: Take a quiz to check your understanding of what you have learned.
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Lesson 8: Similar Solids
- Study - Similar Solids: Learn about similar prisms, pyramids, cylinders, cones, and spheres; the constant ratio between corresponding parts of similar solids; and the ratio of volumes of similar solids.
- Checkup - Practice Problems: Check your understanding of the lesson.
- Quiz - Similar Solids: Take a quiz to check your understanding of what you have learned.
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Lesson 9: Performance Task: Three-Dimensional Solids
- Study - Geodesic Domes: Use your knowledge of three-dimensional solids to solve a geodesic dome problem.
- Project - Performance Task: The Subway Stop: Use what you know about three-dimensional solids to solve a real-world problem.
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Lesson 10: Three-Dimensional Solids Wrap-Up
- Checkup - Three-Dimensional Solids Practice Problems: Check your understanding of the topics in this unit.
- Review - Three-Dimensional Solids: Get ready for the unit test by reviewing important ideas and skills.
- Test (CS) - Three-Dimensional Solids: Take a computer-scored test to check what you have learned in this unit.
- Test (TS) - Three-Dimensional Solids: Take a teacher-scored test to check what you have learned in this unit.
Unit 12: Applications of Probability
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Lesson 1: Probability
- Study - Probability: Explore sample spaces, events, and outcomes. Find probabilities of events and complements of events.
- Checkup - Probability: Check your understanding of the lesson.
- Quiz - Probability: Take a quiz to check your understanding of what you have learned.
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Lesson 2: Probability of Independent and Dependent Events
- Study - Probability of Independent and Dependent Events: Use the general addition rule to find probabilities of compound events. Learn the definitions of independent and dependent events, and classify events as independent or dependent. Find P (A and B) for independent events.
- Checkup - Probability of Independent and Dependent Events: Check your understanding of the lesson.
- Quiz - Probability of Independent and Dependent Events: Take a quiz to check your understanding of what you have learned.
- Journal - Probability of Independent and Dependent Events: Use what you know about independent and dependent events to analyze a real-world problem.
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Lesson 3: Conditional Probability
- Study - Conditional Probability: Learn how to identify and solve conditional probability problems. Use conditional probability concepts to test events for independence.
- Checkup - Conditional Probability: Check your understanding of the lesson.
- Quiz - Conditional Probability: Take a quiz to check your understanding of what you have learned.
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Lesson 4: Two-Way Frequency Tables
- Study - Two-Way Frequency Tables: Identify joint and marginal frequencies. Use two-way tables to find probabilities and conditional probabilities. Use two-way tables to test for independence and to help make decisions.
- Checkup - Two-Way Frequency Tables: Check your understanding of the lesson.
- Quiz - Two-Way Frequency Tables: Take a quiz to check your understanding of what you have learned.
- Practice - Two-Way Frequency Tables: Conduct a survey and use a two-way table to organize and interpret the results.
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Lesson 5: Permutations and Combinations
- Study - Permutations and Combinations: Learn definitions of permutations and combinations. Decide whether a situation involves permutations or combinations. Find the number of permutations or combinations for a given situation. Find probabilities using permutations and combinations.
- Checkup - Permutations and Combinations: Check your understanding of the lesson.
- Quiz - Permutations and Combinations: Take a quiz to check your understanding of what you have learned.
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Lesson 6: Applications of Probability Wrap-Up
- Checkup - Applications of Probability: Check your understanding of the topics in this unit.
- Review - Applications of Probability: Get ready for the unit test by reviewing important ideas and skills.
- Test (CS) - Applications of Probability: Take a computer-scored test to check what you have learned in this unit.
- Test (TS) - Applications of Probability: Take a teacher-scored test to check what you have learned in this unit.
When will this course begin?
Processing time is 1-2 business days. Courses begin each week on Mondays, except for holidays.
Will this class give high school credit?
Yes! Our high school courses are accredited.
Is this course recognized by universities?
Yes! The transcript you receive will come from a fully accredited online school.
Will this class end up on my high school transcript?
Yes, it can! You will need to speak with your academic counselor to get an outside approval request. We will work with you and your school to make sure your high school recognizes our accredited course for placement on your high school transcript.
What if my high school doesn’t give outside credit approval but I still want to take courses that my school doesn’t have to stand out?
No problem! You can still self-report to universities that you took this high school credit course and shine like the shining star that you are.
Will I get support from a live teacher?
Yes! This course comes with support from a certified, experienced teacher available for personalized feedback and assistance Monday-Friday via email and Zoom.
How long does it take to have coursework graded and returned?
Teachers return assignments graded with personalized feedback within 3 business days.
How long will I have to complete this course?
A semester course is scheduled for 9 weeks of access in the summer (May – July) and 18 weeks during the school year (August – April). When you purchase semester 1 and semester 2 courses together, the course is scheduled for 18 weeks in the summer term and 36 weeks during the school year. Students are always welcome to work ahead or add additional time to summer courses (up to 18 weeks for a semester or 36 weeks when semester 1 and semester 2 are purchased together).
Can I finish this course early?
You can complete this course at your pace; so if you get through the coursework quickly, then you can finish early.
What if I need more time to complete this course?
All of our courses are available year-round, and the course content is the same for summer school. Our summer school course duration is set to 9 weeks for semester courses and 18 weeks when semester 1 and semester 2 are purchased together; however, this duration can be extended several weeks upon request.
How can I order my transcript?
All transcripts are available through Parchment, the industry leader in education credentials technology. Parchment is used widely by high schools, colleges, and other academic institutions such as the NCAA. It is a secure service for sending credentials. Transcripts take 1 to 2 business days to process, and you can check online to view the progress of the transaction.
You can use Parchment to order transcripts for multiple institutions at once (including the NCAA). You will automatically receive an unofficial copy for your personal records, and you can track your official transcript. Each Parchment electronic (emailed) transcript costs $5.40, and hard copies sent by mail cost $7.90.
You can use Parchment to order transcripts for multiple institutions at once (including the NCAA). You will automatically receive an unofficial copy for your personal records, and you can track your official transcript. Each Parchment electronic (emailed) transcript costs $5.40, and hard copies sent by mail cost $7.90.
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