Geometry (Plane and Solid Figures)
Geometry questions test angle relationships, properties of triangles and quadrilaterals, circle theorems, congruence and similarity, and the measurement of plane and solid figures.
Core skills
- Use angle facts: angles on a straight line sum to 180°, angles at a point to 360°, and alternate and corresponding angles formed by parallel lines are equal.
- Apply the triangle angle sum (180°) and the exterior angle property.
- Use congruence conditions (SSS, SAS, ASA) and similarity, remembering that similar figures have equal angles and proportional sides.
- Compute areas and volumes: triangle ½×base×height, circle πr², cylinder πr²h, pyramid and cone with the one-third factor.
- Apply the Pythagorean theorem and circle facts such as the inscribed angle being half the central angle on the same arc.
Common traps
Similar figures scale lengths by a factor k but areas by k² and volumes by k³ - a classic error. Students also confuse the slant height of a cone with its vertical height. When using the inscribed-angle theorem, ensure both angles stand on the same arc.
Worked example
Two similar triangles have corresponding sides in ratio 2:3. If the smaller area is 20 cm², the larger area is 20×(3/2)²=20×9/4=45 cm².
Rule of thumb: for similar figures, square the length ratio for area and cube it for volume.