Geometry
Geometry tests triangle and quadrilateral properties, circle theorems, and formal constructions with proofs. SEE answers are marked on correct reasons as well as correct values, so learn theorem statements precisely.
Core rules
- Triangle angle sum =180°; exterior angle equals the sum of the two opposite interior angles.
- Congruence: SSS, SAS, ASA, AAS, RHS. SSA is not a congruence test.
- Similar triangles: corresponding angles equal and corresponding sides proportional.
- Parallelogram: opposite sides and angles equal; diagonals bisect each other. Rectangle diagonals are equal; rhombus diagonals bisect at 90°.
- Circle: angle at centre =2× angle at circumference on the same arc; angles in the same segment are equal; angle in a semicircle =90°; opposite angles of a cyclic quadrilateral are supplementary; tangent is perpendicular to the radius at the point of contact.
- Construction: use a sharp pencil, leave arc marks, and write “construction” lines thinly; give a reason for each proof step.
Worked example
ABCD is a cyclic quadrilateral. If ∠A=110°, find ∠C. Opposite angles of a cyclic quadrilateral are supplementary, so ∠A+∠C=180°. Hence ∠C=180°−110°=70°. The reason must name the cyclic-quadrilateral theorem; merely writing “70°” without the reason often loses the reasoning mark.
Traps
- Assuming a figure is to scale; only given markings count.
- Using SSA to claim congruence.
- Confusing “angle at the centre” with “angle at the circumference”.
- Forgetting that a tangent radius makes 90°.
- Omitting reasons in proofs or giving a theorem name that does not match the step.