Teaching Geometry at home

Prepare before the lesson

1. Read the unit's main idea and work through an example. Identify the earlier skill the method relies on.
2. Choose a short practice set that includes both a familiar example and a changed case. Have paper, a diagram or a number line ready when useful.
3. Locate the worked steps and common mistakes. Decide which step the learner should attempt before you offer a hint.

Teach, discuss and check

1. Ask for a prediction or estimate and a representation before starting an algorithm.
2. Explain one worked step and why it is valid. Let the learner complete the next step with less support.
3. Use an incorrect solution to discuss the reasoning, then give a changed problem without the model in view.
4. Check the result by substitution, units, another representation or an estimate. Ask when the method applies.

Judge the reasoning

Use these discussion criteria with the unit’s own marking guidance. They are a feedback framework, not a universal numerical grade.

• Chooses a suitable representation or relationship.
• Uses valid steps and carries the necessary units or conditions.
• Explains why the method answers the question.
• Checks the result and can adapt to a changed case.

Keep one worked example, one corrected error and one independent changed-case solution. Solving a practice question after retries is progress, but does not by itself establish independent mastery.

When the learner needs support

• When a procedure is memorized without meaning, return to a diagram or a small numerical example.
• When a prerequisite is missing, revisit the matching earlier unit rather than repeating a harder set unchanged.
• Separate an arithmetic slip from a misunderstanding of the relationship, and choose feedback accordingly.

Plan this course

The Regents Geometry course: definitions and proof, triangles and quadrilaterals, similarity and right-triangle trigonometry, circles, coordinate proof, and solids.

This math course has no authored weekly timetable in the Parent Center. Schedule its units or your own activities at a pace you choose.

No authored weekly timetable is available here. Schedule individual units and outside activities at your chosen pace.

Materials and records

Use paper, a suitable diagram or manipulatives, and the worked examples in the existing course.

Use the course assessments

Keep one worked example, one corrected error and one independent changed-case solution. Solving a practice question after retries is progress, but does not by itself establish independent mastery.

Read the full course guide

Units and teaching goals

• Unit 1 · Definitions, Postulates & Reasoning

  Geometry runs on agreed definitions. Once a word is pinned down, arguments about it stop.

• Unit 2 · How to Write a Proof

  A proof is not a calculation. It is a chain of statements where every link carries a reason.

• Unit 3 · Angle Relationships

  Parallel lines cut by a transversal make only two different angles. Knowing which is which unlocks every diagram.

• Unit 4 · Triangle Congruence Proofs

  Six parts make a triangle, but you never need all six. Three of the right kind are enough.

• Unit 5 · Quadrilaterals & Polygon Properties

  The quadrilateral family is a ladder of conditions. Each rung adds one requirement and inherits everything above.

• Unit 6 · Length and Area in 2-D Figures

  Every area formula is a rectangle in disguise. Know where each one comes from and you will never mix them up.

• Unit 7 · Translations, Reflections & Rotations

  Three moves — slide, flip, turn — never change a shape. Everything in this unit follows from that one fact.

• Unit 8 · Dilations & Similarity

  A dilation multiplies every distance from one fixed point by the same number. Angles survive; lengths do not.

• Unit 9 · Similarity & Proportionality

  Equal angles force proportional sides. That single fact measures buildings, mountains and stars.

• Unit 10 · Pythagorean Theorem

  In any right triangle, the two legs squared add to the hypotenuse squared. It turns a right angle into arithmetic.

• Unit 11 · Right Triangle Trigonometry

  One angle and one side are enough to find every other part of a right triangle.

• Unit 12 · Circles

  Every circle has the same ratio of circumference to diameter. That ratio is π, and it drives both formulas.

• Unit 13 · Circle Angles, Arcs & Chords

  Where the vertex of an angle sits — centre, edge or outside — decides which rule applies.

• Unit 14 · Distance on the Coordinate Plane

  Draw the right triangle and the distance formula stops being something to memorise.

• Unit 15 · Equations of Circles

  A circle is every point a fixed distance from a fixed point. Write that with the distance formula and you have its equation.

• Unit 16 · Coordinate Geometry Proofs

  Put a shape on axes and every claim about it becomes a calculation you can check.

• Unit 17 · Geometric Construction

  With only a compass and a straightedge you can copy, bisect and build exactly — and the angle facts tell you when a figure is even possible.

• Unit 18 · Plane Sections of 3-D Figures

  Slice a solid with a flat plane and a flat shape appears. The angle of the cut decides which shape you get.

• Unit 19 · Solids: Volume, Sections & Rotations

  Every solid here is a flat shape that has been stacked, tapered or spun.