GED® Geometry Review

GED® Geometry Review Syllabus

Course Overview

GED® Geometry Review is a complete self-study course for learners who want to
turn geometry formulas into reliable GED® Mathematical Reasoning skills. The
course begins with the decision that comes before every calculation—identifying
what the question actually asks—and then develops area, perimeter,
circumference, volume, surface area, right-triangle, coordinate, and angle
reasoning in a connected sequence.

This is a capstone review, but it does not assume that every formula is already
memorized. Each session rebuilds the idea in plain language, connects it to a
diagram, models a repeatable solving routine, and gives immediate guided and
independent practice. The emphasis is on selecting the right tool, showing a
clear setup, using correct units, and explaining why a tempting answer choice is
wrong.

Course Information

• Program: GED®
• Subject: Mathematical Reasoning / Geometry
• Recommended length: 8 weeks
• Recommended schedule: 3 sessions per week
• Total sessions: 24
• Recommended study time: 60–90 minutes per session
• Visual instruction: 3 responsive SVG geometry diagrams per session
• Guided practice: 10 fully explained worked examples per session
• Lesson assessment: 10 multiple-choice questions per session
• Teacher support: 1 session-specific additional-explanations PDF per session
• Student enrichment: 2 curated external Additional Resources per session
• Cumulative assessment: 47-question mixed final practice bank
• Total lesson questions: 240, with explanations and increasing difficulty

Who This Course Is For

This course is designed for adult GED® learners, returning students, and
independent learners who can perform basic arithmetic but need a structured path
through geometry. Students should be comfortable with whole numbers, decimals,
fractions, and calculator entry. No previous geometry course is required, but
learners should be willing to draw quick sketches, label units, and keep an error
log.

Course Materials

• This course's 24 SVG-supported lessons and practice sets
• A notebook or digital document for formulas, sketches, and an error log
• Pencil, scratch paper, ruler, and optional graph paper
• A scientific calculator or the GED®-style onscreen calculator
• The official GED® formula sheet and calculator reference sheet
• Optional index cards for formulas, clue words, angle rules, and common triples

Course Problem-Solving Method

Use the same five-stage routine throughout the course:

1. Classify: Identify the requested measurement or relationship.
2. Sketch and label: Mark the shape, dimensions, right angles, parallel
   lines, coordinates, and units.
3. Plan: Select a formula or rule and predict the answer's unit and
   approximate size.
4. Solve: Substitute carefully, calculate in a logical order, and round only
   when required.
5. Check: Confirm the unit, reasonableness, diagram markings, and wording of
   the original question.

Complete Course Outline

How to Study Each Session

1. Read the opening explanation and say the session's main idea in your own
   words.
2. Work through the learning targets and copy the solving routine into your
   notebook.
3. Study all three diagrams. Identify what each label means before reading its
   caption.
4. Rework the GED® application without looking at the solution.
5. Cover the answers and attempt the 10 worked examples independently.
6. Complete the 10 lesson MCQs without notes.
7. Review every explanation, including questions answered correctly by guessing.
8. Record each miss as a classification, formula/rule, diagram,
   arithmetic, or unit error.
9. Redo missed questions after 24–48 hours and again during the weekly mixed
   review.

Assessment and Mastery Plan

• Lesson checks: 10 MCQs in every session, moving from foundation to harder
  GED®-style reasoning.
• Session mastery target: At least 8 out of 10 without notes.
• Correction requirement: Explain the correct setup and the specific reason
  for every missed answer.
• Cumulative practice: 47 mixed questions spanning all geometry strands.
• Course completion target: Complete all 24 sessions, correct every logged
  error, and reach at least 80% on cumulative practice.

The percentages below are course-practice signals, not official GED® score
conversions.

Course Expectations

• Draw and label a diagram even when the question provides one.
• Write the formula or rule before entering numbers into a calculator.
• Include units on every final answer and intermediate measurement.
• Use diagram markings as evidence; never assume a figure is drawn to scale.
• Keep all scratch work until corrections are complete.
• Treat mistakes as data for the next study session, not as a final judgment of
  ability.

Completion Standard

A student completes the course by finishing all lesson practice, maintaining an
error log, correcting missed questions with written reasoning, and attempting
the cumulative practice bank. Strong completion means the student can explain
not only how a calculation works, but also why that calculation answers the
question that was asked.

GED® Geometry Review Course Outcomes

By the end of this course, students will be able to demonstrate the following
measurable outcomes.

Measurement and Model Selection

• Classify a geometry question as length, perimeter, circumference, area,
  surface area, volume, coordinate distance, or angle measure before calculating.
• Translate real-world clue words into an appropriate geometry model without
  depending on clue words alone.
• Predict whether an answer should use plain, square, cubic, or degree units.
• Convert compatible measurements to a common unit and carry units correctly
  through multi-step work.

Area, Perimeter, and Circles

• Calculate and explain the area of rectangles, squares, triangles,
  parallelograms, trapezoids, circles, and composite figures.
• Identify a perpendicular height even when a triangle or quadrilateral is
  tilted or the height lies outside the shape.
• Calculate polygon perimeter by tracing every exterior segment exactly once and
  infer missing boundary lengths from aligned dimensions.
• Distinguish circle radius from diameter and select efficiently between circle
  area and circumference formulas.
• Estimate area and circumference to identify unreasonable calculator results.

Volume and Surface Area

• Model prism and cylinder volume as base area times perpendicular height.
• Calculate volume for boxes, cubes, prisms, cylinders, cones, and spheres using
  correct cubic units.
• Interpret nets and calculate the surface area of boxes, cubes, and cylinders.
• Adjust surface-area calculations for open, missing, attached, or unexposed
  faces.
• Distinguish inside capacity from outside covering in real-world problems and
  apply rates, cost, or material quantities after the geometry calculation.

Right Triangles and Coordinate Geometry

• Verify that a triangle is right, identify the hypotenuse, and apply the
  Pythagorean theorem to find missing lengths.
• Find missing legs by subtracting squares and use common Pythagorean triples as
  efficient checks.
• Model rectangle diagonals, ladders, and coordinate distances as right-triangle
  problems.
• Plot and interpret ordered pairs, axes, quadrants, horizontal distances, and
  vertical distances.
• Select and use distance, midpoint, or slope based on the wording and purpose of
  a coordinate problem.
• Interpret positive, negative, zero, and undefined slopes from graphical
  evidence.

Angles and Triangles

• Classify angle types and use 90-degree, 180-degree, and 360-degree benchmark
  sums.
• Solve for vertical angles and linear pairs, including problems with algebraic
  expressions.
• Recognize corresponding, alternate interior, and same-side interior angles
  formed by parallel lines and a transversal.
• Apply triangle interior-angle and exterior-angle relationships.
• Use isosceles, equilateral, and right-triangle properties only when diagram
  markings or stated information justify them.
• Check that side and angle relationships are consistent, including the fact
  that the longest side lies opposite the largest angle.

GED®-Style Problem Solving and Independent Learning

• Follow a repeatable classify–sketch–plan–solve–check process on unfamiliar
  geometry questions.
• Move among words, diagrams, tables, formulas, and coordinate graphs without
  changing the meaning of the problem.
• Eliminate distractors by identifying wrong formulas, missing factors,
  radius/diameter confusion, unit errors, and unsupported diagram assumptions.
• Use estimation, inverse operations, alternate decompositions, and formula
  substitution to verify answers.
• Maintain an error log, categorize the source of mistakes, and select an
  appropriate session for targeted review.
• Complete mixed geometry practice with at least 80% accuracy and explain the
  reasoning behind corrected answers.