Geometry: Angles, Triangles, Circles and Solids
What you must command
Geometry rewards precise vocabulary and a habit of stating reasons. You should know angle facts for straight lines, around a point, in triangles and quadrilaterals, and for parallel lines cut by a transversal: corresponding, alternate and co-interior angles. Know the properties of isosceles, equilateral and right-angled triangles, congruence and similarity, and Pythagoras' theorem. For circles, be confident with circumference, arc length, area and sector area, and the relationships between radius, diameter and tangent. For solids, handle volume and surface area of prisms, cylinders, cones and spheres, and convert between units of area and volume.
Traps that catch candidates
- Area conversion squares the factor: 1 square metre is 10,000 square centimetres, not 100.
- Volume conversion cubes it: 1 cubic metre is 1,000,000 cubic centimetres.
- Sector area uses the fraction of the full circle, so the angle over 360 multiplies the full area.
- Pythagoras applies only to right-angled triangles, and the hypotenuse is the longest side opposite the right angle.
- Similar figures scale lengths by k, areas by k squared and volumes by k cubed.
- Give a reason for every angle you claim; unexplained values lose marks.
Worked example
A sector has radius 6 cm and angle 60 degrees. Full area = pi times 36, approximately 113.1 square centimetres. The fraction is 60/360 = 1/6, so sector area is about 18.8 square centimetres. Arc length is 1/6 of the circumference, about 6.3 cm.
Rule of thumb
Sketch, label known values and mark the unknown, then write the fact or formula you will use before substituting. This turns a geometry answer into a short, mark-earning argument.