Mathematics

Geometry: scope and sequence

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

There is no fixed calendar for this course. The units are written to be taken in order, and most families spend one to two weeks on each.

The units, in order

#	Unit and what it covers	Lessons
1	Definitions, Postulates & Reasoning Geometry runs on agreed definitions. Once a word is pinned down, arguments about it stop.	5
2	How to Write a Proof A proof is not a calculation. It is a chain of statements where every link carries a reason.	5
3	Angle Relationships Parallel lines cut by a transversal make only two different angles. Knowing which is which unlocks every diagram.	4
4	Triangle Congruence Proofs Six parts make a triangle, but you never need all six. Three of the right kind are enough.	5
5	Quadrilaterals & Polygon Properties The quadrilateral family is a ladder of conditions. Each rung adds one requirement and inherits everything above.	5
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.	5
7	Translations, Reflections & Rotations Three moves — slide, flip, turn — never change a shape. Everything in this unit follows from that one fact.	5
8	Dilations & Similarity A dilation multiplies every distance from one fixed point by the same number. Angles survive; lengths do not.	4
9	Similarity & Proportionality Equal angles force proportional sides. That single fact measures buildings, mountains and stars.	5
10	Pythagorean Theorem In any right triangle, the two legs squared add to the hypotenuse squared. It turns a right angle into arithmetic.	6
11	Right Triangle Trigonometry One angle and one side are enough to find every other part of a right triangle.	6
12	Circles Every circle has the same ratio of circumference to diameter. That ratio is $\pi$, and it drives both formulas.	5
13	Circle Angles, Arcs & Chords Where the vertex of an angle sits — centre, edge or outside — decides which rule applies.	5
14	Distance on the Coordinate Plane Draw the right triangle and the distance formula stops being something to memorise.	4
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.	5
16	Coordinate Geometry Proofs Put a shape on axes and every claim about it becomes a calculation you can check.	5
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.	5
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.	5
19	Solids: Volume, Sections & Rotations Every solid here is a flat shape that has been stacked, tapered or spun.	5

Open Geometry · All courses