Similar Figures — Quick Reference Cheatsheet
A focused companion to the main Similar Figures topic page on ACT Math.
ACT Math Plane Geometry One-page reference
This is a one-page reference for Similar Figures on the ACT math section. Use side-ratio and area-ratio properties of similar polygons (k for sides, k² for area, k³ for volume). Use it as a printable cheatsheet before test day, or as a refresher right before you attempt the worked questions on the main Similar Figures topic page.
What this topic is
A Similar Figures question tests triangles, quadrilaterals, circles, and 3-D solids. The ACT gives you NO reference sheet — every formula must be in your head.
Core formulas you must memorise
- Triangle area: ½ b h
- Pythagorean: a² + b² = c²
- Circle: A = πr², C = 2πr
- Sum of interior angles: (n − 2) · 180°
- Volume cylinder: πr²h ; sphere: ⁴⁄₃πr³ ; cone: ⅓πr²h
If any of these formulas are not yet automatic, drill them via the Plane Geometry 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
ACT questions on Similar Figures 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 Similar Figures 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
Always re-draw the diagram on your scratch with all known values labelled. The labelling alone solves a quarter of plane-geometry questions.
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 Similar Figures 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 Similar Figures strategy guide. For category-wide context, browse all Plane Geometry topics. For score-targeted study plans, see the score-band guides.