Geometry is a critical mathematics course that builds upon the foundational skills developed in Algebra I and introduces students to the study of spatial relationships and logical reasoning. Geometry helps students understand and apply the properties and relationships of points, lines, planes, angles, surfaces, and solids. It serves as an essential bridge between basic arithmetic skills and the higher-level abstract thinking required in advanced mathematics and science courses.
The course emphasizes both visual and analytical problem solving. Students will explore topics such as congruence, similarity, properties of triangles, circles, coordinate geometry, right triangle trigonometry, and transformations. Key learning outcomes include the ability to:
- Construct logical arguments and formal proofs
- Solve problems involving geometric figures and measurements
- Apply coordinate systems to model geometric concepts
- Analyze the properties and relationships of two- and three-dimensional objects
- Explore the connections between geometry and algebra through transformations and coordinate methods
Students cultivate critical thinking by using deductive reasoning, constructing proofs, and validating solutions systematically. Geometry strengthens mathematical communication skills and nurtures the precision needed for success in fields such as computer science, engineering, architecture, and physics.
At 2Sigma School, Geometry is taught through a project-based approach where students engage in investigations, constructions, and modeling activities. Projects may include designing structures using geometric principles, creating scaled models, or exploring the mathematics behind art, design, and navigation systems. Students move beyond rote memorization and learn how geometry applies to the world around them.
It is recommended that students have successfully completed Algebra I prior to beginning Geometry. The highest performing students enjoy logical analysis, structured argumentation, and visual reasoning. Geometry is not just about shapes—it's about developing a structured way of thinking that enables students to approach problems methodically and creatively.
Course Outline
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Constructions and Rigid Transformations
This unit introduces students to the fundamental tools of geometry, the compass and straightedge, and how to use them to create geometric figures. Students explore rigid transformations like translations, reflections, and rotations, developing an understanding of how these transformations preserve distance and angles. The unit culminates in students using transformations and constructions as a basis for developing geometric arguments and proofs.
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Congruence
In this unit, students delve into the concept of congruence, focusing primarily on triangles and extending to quadrilaterals. Students use rigid transformations to establish the conditions for triangle congruence, such as SSS, SAS, and ASA. They apply these congruence criteria to prove geometric relationships and solve problems involving congruent figures.
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Similarity
This unit explores the concept of similarity, which involves figures that have the same shape but not necessarily the same size. Students investigate dilations and their properties, using them to define similarity transformations. Students develop an understanding of proportional reasoning in the context of similar figures and apply these concepts to solve problems, including those involving right triangles.
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Right Triangle Trigonometry
This unit introduces students to trigonometry, the study of relationships between angles and side lengths in triangles. Students begin by examining the concept of 'steepness' and how it relates to angles, leading to the definition of trigonometric ratios: sine, cosine, and tangent. Students apply these ratios to solve problems involving right triangles, finding missing side lengths and angle measures.
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Solid Geometry
In this unit, students extend their understanding of geometry from two dimensions to three dimensions. Students explore cross-sections of three-dimensional figures and how scaling affects area and volume. The unit focuses on calculating the volumes of prisms, cylinders, pyramids, and other solid figures.
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Coordinate Geometry
This unit connects algebra and geometry by exploring geometric concepts within the coordinate plane. Students use transformations to analyze figures, calculate distances, and derive equations of circles and parabolas. A key focus is on using algebraic methods to prove geometric theorems, strengthening the connection between these two branches of mathematics.
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Circles
This unit delves into the properties of circles, including the relationships between lines, angles, and arcs within a circle. Students investigate inscribed and circumscribed polygons and develop an understanding of how to measure circles, including finding circumference, arc length, and area.
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Conditional Probability
This unit introduces students to the fundamental concepts of probability. Students learn to calculate the likelihood of events, explore how events can be combined, and analyze the relationships between events, including conditional probability.
To take any of our courses, students must be familiar with opening a browser, navigating to a website, and joining a Zoom meeting.
Students must have a quiet place to study and participate in the class for the duration of the class. Some students may prefer a headset to isolate any background noise and help them focus in class.
Most course lectures and content may be viewed on mobile devices but programming assignments and certain quizzes require a desktop or laptop computer.
Students are required to have their camera on at all times during the class, unless they have an explicit exception approved by their parent or legal guardian.
Our technology requirements are similar to that of most Online classes.
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A desktop or laptop computer running Windows (PC), Mac OS (Mac), or Chrome OS (Chromebook).
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Students must be able to run a Zoom Client. |
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A working microphone, speaker, webcam, and an external mouse. |
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A high-speed internet connection with at least 15mbps download speed (check your Internet speed). |
This course includes several timed tests where you will be asked to complete a given number of questions within a 1-3 hour time limit. These tests are designed to keep you competitively prepared but you can take them as often as you like. We do not proctor
these exams, neither do we require that you install special lockdown browser.
In today's environment, when students have access to multiple devices, most attempts to avoid cheating in online exams are symbolic. Our exams are meant to encourage you to learn and push yourself using an honor system.
We do assign a grade at the end of the year based on a number of criteria which includes class participation, completion of assignments, and performance in the tests. We do not reveal the exact formula to minimize students' incentive to optimize for a
higher grade.
We believe that your grade in the course should reflect how well you have learnt the skills, and a couple of timed-tests, while traditional, aren't the best way to evaluate your learning.