Geometry
The Regents Geometry course: definitions and proof, triangles and quadrilaterals, similarity and right-triangle trigonometry, circles, coordinate proof, and solids.
Geometry covers 19 units across 2 strands, with 304 practice questions, worked examples, and a printable page for every unit. Each unit has a lesson, practice with worked steps, challenge problems, and a chapter review; the course has chapter quizzes, a midterm and a final.
Every unit below is a page of its own: read the explanation, work the examples, then practise. Answers and worked steps are shown after each attempt, so a parent does not have to mark the routine questions.
Units in Geometry
- Definitions, Postulates & Reasoning — Geometry runs on agreed definitions. Once a word is pinned down, arguments about it stop.
- How to Write a Proof — A proof is not a calculation. It is a chain of statements where every link carries a reason.
- Angle Relationships — Parallel lines cut by a transversal make only two different angles. Knowing which is which unlocks every diagram.
- Triangle Congruence Proofs — Six parts make a triangle, but you never need all six. Three of the right kind are enough.
- Quadrilaterals & Polygon Properties — The quadrilateral family is a ladder of conditions. Each rung adds one requirement and inherits everything above.
- 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.
- Translations, Reflections & Rotations — Three moves — slide, flip, turn — never change a shape. Everything in this unit follows from that one fact.
- Dilations & Similarity — A dilation multiplies every distance from one fixed point by the same number. Angles survive; lengths do not.
- Similarity & Proportionality — Equal angles force proportional sides. That single fact measures buildings, mountains and stars.
- Pythagorean Theorem — In any right triangle, the two legs squared add to the hypotenuse squared. It turns a right angle into arithmetic.
- Right Triangle Trigonometry — One angle and one side are enough to find every other part of a right triangle.
- Circles — Every circle has the same ratio of circumference to diameter. That ratio is π, and it drives both formulas.
- Circle Angles, Arcs & Chords — Where the vertex of an angle sits — centre, edge or outside — decides which rule applies.
- Distance on the Coordinate Plane — Draw the right triangle and the distance formula stops being something to memorise.
- 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.
- Coordinate Geometry Proofs — Put a shape on axes and every claim about it becomes a calculation you can check.
- 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.
- 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.
- Solids: Volume, Sections & Rotations — Every solid here is a flat shape that has been stacked, tapered or spun.