Geometry and Trigonometry
What to know
Both synthetic and coordinate geometry appear. Know angle relationships formed by parallel lines and transversals, triangle congruence and similarity criteria, the Pythagorean theorem and its converse, special right triangles (45-45-90 and 30-60-90), perimeter, area, surface area, and volume formulas, and the scaling laws: lengths scale by k, areas by k², and volumes by k³. Circle theorems matter - an inscribed angle is half its central angle, a radius meets a tangent perpendicularly at the point of tangency, and chords, secants, and tangents generate predictable arc and angle relationships. Coordinate geometry brings distance, midpoint, slope, line and circle equations, and transformations including rotations and dilations. Trigonometry spans right-triangle ratios, the unit circle, degree-radian conversion, graphs, identities (Pythagorean, reciprocal, quotient), and the law of sines and law of cosines.
Traps
- The law of sines is ambiguous in the SSA case: two triangles, one triangle, or none may exist.
- Calculator mode (degree versus radian) silently corrupts trig values.
- An inscribed angle subtending a diameter is 90°, a special case that is easy to miss.
- Similar figures do not preserve area or volume in the ratio k.
- sin²θ means (sin θ)², while sin⁻¹θ means arcsine, not 1/sin θ.
Worked example
A cone has volume 24 cm³. A similar cone has twice the radius and twice the height. Because volumes scale by k³ = 2³ = 8, the new volume is 24 × 8 = 192 cm³ - not 24 × 2 = 48 cm³.