# Geometry study guides

Canonical: https://duckyhelper.com/learn/geometry/
Updated: 2026-10-01

Seven guides in the order most geometry classes teach them. Each one starts with a short, plain answer, then works through examples step by step, lists the mistakes that cost points, and ends with five practice questions with explained answers. Every worked example and practice answer on these pages is checked by code.

- [Angles, parallel lines and polygon angle sums](https://duckyhelper.com/learn/geometry/angles-and-parallel-lines/): Corresponding, alternate interior and same-side angles, triangle angle sums, exterior angles and polygon angle sums. Worked examples and 5 practice questions.
- [Triangle congruence: SSS, SAS, ASA, AAS and HL](https://duckyhelper.com/learn/geometry/triangle-congruence/): How to prove triangles congruent with SSS, SAS, ASA, AAS and HL, why SSA fails, what CPCTC means, and a two-column proof. Worked examples and practice.
- [Similar triangles and scale factor](https://duckyhelper.com/learn/geometry/similar-triangles/): How to prove triangles similar (AA, SAS, SSS), set up proportions that work, and scale areas and volumes. Worked examples and 5 practice questions.
- [The Pythagorean theorem](https://duckyhelper.com/learn/geometry/pythagorean-theorem/): Use the Pythagorean theorem to find any side of a right triangle, spot triples, classify triangles with the converse and find distances. With practice.
- [Special right triangles: 45-45-90 and 30-60-90](https://duckyhelper.com/learn/geometry/special-right-triangles/): The side ratios for 45-45-90 and 30-60-90 triangles, where they come from, and how to use them, including rationalizing. Worked examples and practice.
- [Right triangle trigonometry and SOHCAHTOA](https://duckyhelper.com/learn/geometry/right-triangle-trigonometry/): Use sine, cosine and tangent (SOHCAHTOA) to find sides and angles of right triangles, with inverse trig, angles of elevation and cofunctions. With practice.
- [Circle theorems: angles, chords, tangents and arcs](https://duckyhelper.com/learn/geometry/circle-theorems/): Central and inscribed angles, arcs, chords and tangents, plus arc length and sector area in degrees. Clear rules, worked examples and 5 practice questions.

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