Properties of Triangles — Quick Reference Cheatsheet
A focused companion to the main Properties of Triangles topic page on SAT Math.
SAT Math Geometry & Trigonometry One-page reference
This is a one-page reference for Properties of Triangles on the SAT math section. Use the triangle angle-sum, the exterior-angle theorem and the triangle inequality. Use it as a printable cheatsheet before test day, or as a refresher right before you attempt the worked questions on the main Properties of Triangles topic page.
What this topic is
A Properties of Triangles question tests your ability to apply geometric formulas, recognise special triangles, and use right-triangle trigonometry. Sketch the diagram before computing — every time.
Core formulas you must memorise
- Pythagorean: a² + b² = c²
- 30-60-90 sides: 1 : √3 : 2
- 45-45-90 sides: 1 : 1 : √2
- Circle: A = πr² ; C = 2πr
- SOH-CAH-TOA
- Pythagorean identity: sin²θ + cos²θ = 1
If any of these formulas are not yet automatic, drill them via the Geometry & Trigonometry formula sheet. Memorisation is fastest when you write each formula out by hand five times in a row, then quiz yourself the next morning.
How to spot this question type on the test
SAT questions on Properties of Triangles typically present in one of three ways: as a pure symbolic problem ("solve for x"), wrapped in a word problem (a real-world scenario you must translate), or hidden inside a longer multi-step question where Properties of Triangles is just the first or last step. Train yourself to recognise the signature — a particular word, equation form, or diagram — and you will halve your reading time.
The 30-second decision
The SAT reference sheet gives you area and volume formulas but NOT the trig identities or the equation of a circle. Memorise those.
If you have 60 seconds before the question
Glance at the answer choices first. If they are widely spaced, estimate; if they are close, you must be exact. Sketch any diagram involved. Identify which of the formulas above applies. Then attempt — and if you cannot finish in 90 seconds, mark and move on. There is no penalty for guessing on either the SAT or the ACT, so always bubble in.
Drill set
Re-attempt the six worked Properties of Triangles questions with this cheatsheet open. Then close it and re-attempt them from memory. If you can solve all six without peeking, this topic is locked in.
Related study material
For broader test-prep tactics, see our Properties of Triangles strategy guide. For category-wide context, browse all Geometry & Trigonometry topics. For score-targeted study plans, see the score-band guides.