Geometry
What you must understand
Geometry questions test angle relationships, triangle congruence and similarity, the Pythagorean theorem, area and volume formulas, coordinate geometry, and circle properties. You should be able to compute distances and midpoints, use slope to identify parallel and perpendicular lines, apply similarity ratios to lengths and areas, and reason about inscribed angles and arcs.
Traps that appear in questions
- Similarity scaling. If lengths scale by k, areas scale by k² and volumes by k³. Doubling a side quadruples the area.
- Complementary vs supplementary. Two angles summing to 90° are complementary; 180° are supplementary.
- Inscribed angle theorem. An inscribed angle is half its intercepted arc, not equal to it.
- Slope of perpendicular lines. Perpendicular slopes are negative reciprocals, not just negatives.
- Degrees vs radians in trigonometric applications.
Worked example
Two similar triangles have corresponding sides in ratio 3:5. If the smaller triangle has area 18, the larger area is 18 × (5/3)² = 18 × 25/9 = 50. Rule of thumb: apply the square of the length ratio to areas and the cube to volumes.
Coordinate geometry
Use the distance formula √((x₂−x₁)² + (y₂−y₁)²) and midpoint ((x₁+x₂)/2, (y₁+y₂)/2). Parallel lines share slope; perpendicular lines multiply to −1. Draw a quick sketch to catch impossible configurations before computing.