Planimetry
Core concepts
Master triangle congruence and similarity, the Pythagorean theorem, Thales' theorem, the sine and cosine rules, area formulas (½ab sin C, Heron's formula), and properties of circles: inscribed angles, tangents, chord properties, and the power of a point. Know properties of parallelograms, trapezoids, and regular polygons, and the sum of interior angles of an n-gon (n − 2)·180°.
Traps
- Applying similarity ratios to areas without squaring (areas scale as the square of the ratio).
- Forgetting that the inscribed angle equals half the central angle subtending the same arc.
- Using the sine rule when the cosine rule is appropriate (two sides plus the included angle).
- Ambiguous case of the sine rule: two possible triangles when given SSA.
- Mixing up the radius and diameter in circle formulas.
Worked example
In triangle ABC, AB = 7, AC = 9, and angle A = 60°. Find BC. By the cosine rule: BC² = 7² + 9² − 2·7·9·cos 60° = 49 + 81 − 63 = 67, so BC = √67.
Rule of thumb
Choose the cosine rule when you know two sides and the included angle (or all three sides); choose the sine rule when you know a side and its opposite angle.