Euclidean Geometry
Euclidean Geometry covers the basic axioms and postulates, angle relationships formed by transversals, triangle properties, and the congruence criteria used in formal proofs. Marks depend on stating the correct reason, not only the conclusion.
Core rules
- Through two distinct points there is exactly one straight line; a line segment can be extended indefinitely.
- Angles on a straight line sum to 180°; angles around a point sum to 360°.
- When a transversal cuts two parallel lines, corresponding angles are equal, alternate interior angles are equal, and co-interior angles sum to 180°.
- The exterior angle of a triangle equals the sum of the two interior opposite angles.
- Congruence criteria: SSS, SAS, ASA, AAS and RHS. AAA and SSA are not congruence criteria.
Worked example
Two parallel lines are cut by a transversal. One co-interior angle is 3x and the other is 2x + 30. Since co-interior angles are supplementary, 3x + (2x + 30) = 180, so 5x = 150 and x = 30. The angles are 90° and 90°, which is consistent because the transversal is then perpendicular to the parallel lines.
Traps
Do not call alternate angles “corresponding” in a proof; examiners award the reason mark separately. A figure that looks isosceles is not isosceles unless given or proved. When using SAS, the included angle must lie between the two stated sides. Never assume lines are parallel because they look parallel.