Geometry and Spatial Sense
What you must understand
Geometry questions test both reasoning and recall. You need the angle facts for straight lines, points, triangles and parallel lines (alternate, corresponding, co-interior), properties of polygons including interior and exterior angle sums, symmetry, congruence and similarity, circle theorems, bearings, and coordinate geometry of straight lines. You should be able to construct and interpret scale drawings and identify transformations: reflection, rotation, translation and enlargement, including the centre and scale factor.
Traps that appear in questions
- Angle reasons. Give a reason for every angle statement; unexplained answers lose marks.
- Parallel lines. Alternate and corresponding angles are equal, but co-interior angles sum to 180°.
- Similar versus congruent. Similar shapes have equal angles and proportional sides; congruent shapes are identical in size and shape.
- Bearings. Measured clockwise from north, written with three digits, and always taken at the starting point.
- Enlargement. A negative scale factor places the image on the opposite side of the centre.
- Polygon formulae. Interior angle sum = (n − 2) × 180°; exterior angle sum is always 360°.
Worked example
A regular polygon has an exterior angle of 24°. The number of sides is 360 ÷ 24 = 15. Each interior angle is 180 − 24 = 156°, and the interior angle sum is 15 × 156 = 2340°, which agrees with (15 − 2) × 180 = 2340°.
Rule of thumb
Before calculating, mark every known angle on the diagram, then ask which single fact (straight line, triangle, parallel lines, circle) links it to the unknown.