GED® Geometry: Pythagorean Theorem & Coordinate Geometry
A complete GED® Geometry course connecting right triangles to the coordinate plane. Students learn to identify and model right triangles; find a hypotenuse or missing leg; use and verify Pythagorean triples; estimate non-perfect square roots; and solve authentic distance problems. On the coordinate plane, they plot points, measure grid segments, use distance and midpoint formulas, recover missing endpoints, calculate and interpret slope, and select the correct tool in multi-step problems. Lessons include diagrams, concept notes, worked examples, error analysis, calculator guidance, GED®-style strategy, and interactive self-checks. Lesson practice and a cumulative final provide detailed teaching explanations.
📚 Course Curriculum
Learning goals. By the end of this lesson, you should be able to:. identify the right angle, two legs, and hypotenuse in any orientation;. explain …
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Learning goals. By the end of this lesson, you should be able to:. state the Pythagorean Theorem with \(c\) as the hypotenuse;. explain the theorem …
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Learning goals. By the end of this lesson, you should be able to:. find a hypotenuse from two legs;. report exact and rounded answers appropriately; …
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Learning goals. By the end of this lesson, you should be able to:. distinguish a missing-leg problem from a missing-hypotenuse problem;. isolate and calculate a …
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Learning goals. By the end of this lesson, you should be able to:. recognize the most useful Pythagorean triples;. scale a triple up or down …
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Learning goals. By the end of this lesson, you should be able to:. translate a situation into a labeled right triangle;. distinguish travel distance from …
Open trial session →Learning goals. By the end of this lesson, you should be able to:. plot and read ordered pairs without reversing coordinates;. classify points by quadrant …
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Learning goals. By the end of this lesson, you should be able to:. find horizontal and vertical lengths using absolute differences;. use the scale of …
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Learning goals. By the end of this lesson, you should be able to:. derive and apply the distance formula;. distinguish exact distance, squared distance, and …
Open trial session →Learning goals. By the end of this lesson, you should be able to:. find a midpoint by averaging coordinates;. recover a missing endpoint when the …
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Learning goals. By the end of this lesson, you should be able to:. calculate slope from two points using a consistent subtraction order;. interpret positive, …
Open trial session →Learning goals. By the end of this lesson, you should be able to:. select a formula from the quantity requested, not just the numbers shown;. …
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Course Syllabus
This self-paced GED® Math course follows a 12-lesson sequence. Work through the modules in order so that each skill supports the next.
Course sequence
Module 1 - Lessons 1-4
- Right Triangles: Legs and Hypotenuse
- The Pythagorean Theorem: a² + b² = c²
- Finding the Hypotenuse
- Finding a Missing Leg
Module 2 - Lessons 5-8
- Pythagorean Triples: Useful Shortcuts
- Real-World Pythagorean Problems
- The Coordinate Plane: Points and Quadrants
- Distance Along the Grid: Horizontal and Vertical
Module 3 - Lessons 9-12
- The Distance Formula
- The Midpoint Formula
- Slope on the Coordinate Plane
- Strategy: Which Tool, and When
Practice and completion
- Use worked examples and lesson practice to check understanding after each module.
- Review incorrect answers, explain the correction, and repeat weak skills.
- Complete the available mixed or final course practice to demonstrate readiness.
Course Outcomes
By the end of this course, learners will be able to:
- Explain and apply the mathematical ideas in Right Triangles: Legs and Hypotenuse.
- Solve multi-step problems involving Finding a Missing Leg and show a clear method.
- Interpret representations and check the reasonableness of work involving The Coordinate Plane: Points and Quadrants.
- Choose efficient strategies for unfamiliar questions related to The Distance Formula.
- Combine skills from Strategy: Which Tool, and When with earlier topics in mixed practice.
- Use feedback and answer explanations to diagnose and correct mistakes.
- Complete mixed, exam-style practice with clearer reasoning and greater independence.
📝 Practice Questions
286 interactive questions with instant feedback and explanations.
Enroll for free to unlock the full practice bank after the trial sessions.