Geometry
What you must know
Learn angle facts and use them in chains of reasoning: angles on a straight line (180 degrees), at a point (360 degrees), vertically opposite, and in parallel lines (alternate, corresponding and co-interior angles). Triangle angle sum is 180 degrees; the exterior angle equals the sum of the two opposite interior angles. For polygons, exterior angles sum to 360 degrees and interior angles to (n - 2) x 180 degrees. Know the circle theorems: angle at the centre is twice the angle at the circumference, angle in a semicircle is 90 degrees, angles in the same segment are equal, opposite angles of a cyclic quadrilateral sum to 180 degrees, tangent perpendicular to radius, and alternate segment theorem. Be able to construct a perpendicular bisector, an angle bisector and a locus, and describe transformations fully: reflection (mirror line), rotation (centre, angle, direction), translation (column vector), enlargement (centre and scale factor, including negative and fractional). Work confidently with column vectors: addition, scalar multiplication, magnitude and the parallel condition.
Traps
- Give a reason for each angle you calculate; unexplained answers often lose marks.
- In rotation, state direction (clockwise or anticlockwise) and angle.
- Enlargement with scale factor k multiplies area by k^2 and volume by k^3.
- Alternate segment angles involve the tangent and a chord, not two chords.
- Bearings are measured clockwise from north as three figures, for example 045 degrees.
Rule of thumb
Mark every known angle on the diagram, then ask which theorem or angle fact links it to the target angle.
Example: each interior angle of a regular 12-sided polygon = (12 - 2) x 180 degrees / 12 = 150 degrees.