Master Geometry from first principles
Lines, angles, triangles, circles, proofs, and trigonometry. Aligned to the Massachusetts Curriculum Frameworks for Geometry.
Geometry — Essential Formulas (Quick Reference)
Triangle theorems, circle formulas, area and volume, coordinate geometry, and trig — all the Geometry Regents essentials on one page.
Parallel Lines & Transversals: The Eight Angles, Three Rules
When a transversal cuts two parallel lines, eight angles appear — but they're really just two values repeating. The three rules that turn every angle problem into a one-step calculation.
The Pythagorean Theorem: One Equation, Half the Geometry Regents
The most-tested theorem in New York Geometry, derived visually. Find missing sides, recognize the five triples by sight, and avoid the two classic traps that cost students easy points.
Special Right Triangles: 30-60-90 and 45-45-90 Without a Calculator
The two right-triangle shapes the New York Regents loves to test. Memorize one ratio for each and skip the Pythagorean arithmetic on roughly 1 in 6 Geometry questions.
SOH-CAH-TOA: Sin, Cos, Tan from First Principles
Three ratios, one angle, every right-triangle problem. The visual lesson that turns sin/cos/tan from a memorization headache into a 5-second decision.
Triangle Congruence & Similarity: SSS, SAS, ASA, AA and the Famous Traps
When are two triangles identical, when are they just scaled copies, and why do AAA and SSA never prove congruence? The five valid rules, the AA shortcut for similarity, and the k² / k³ area-and-volume scaling rule.
Quadrilaterals & Parallelograms: The Family Tree of Four-Sided Shapes
Square, rectangle, rhombus, parallelogram, trapezoid, kite — they're all related, and the relationship is the test. Learn the hierarchy and you'll never miss a 'must be / could be' question.
Coordinate Geometry & Transformations: Move, Flip, Spin, Scale
Translate, reflect, rotate, dilate — the four moves on the coordinate plane and the rules for each. Plus the distance, midpoint, and slope formulas you need on every coordinate question.
Circles: Arcs, Chords, Tangents, and Inscribed Angles
The Geometry Regents has a whole NYS category just for circles. Master the central-angle / inscribed-angle / tangent rules and the circle-equation form (x − h)² + (y − k)² = r².
Surface Area & Volume: Six Shapes, Six Formulas, One Strategy
Cylinder, cone, sphere, prism, pyramid — the formulas and the visual cues. Plus the scaling rule that explains why doubling dimensions multiplies volume by 8.
Two-Column Proofs: How to Argue Geometry Like a Mathematician
Statement, reason. Statement, reason. Two-column proofs aren't a memorization task — they're a logic format. Here's how to recognize when each rule applies and how to chain them into a valid argument.