6 Geometry

Geometrical properties of Euclidean space, as listed below In solving any problem or rider, students may use any knowledge they possess Solutions may be by traditional methods (e.g. congruent triangles), vectors, the use of transformations such as translation, reflection, rotation and enlargement, or a mixture of these Formal proofs of theorems will not be required

Geometrical reasoning

Angle properties of parallel lines, triangles and polygons, including regular polygons Angles on a straight line, angles around a point Angles measured anticlockwise will be taken as positive; clockwise as negative

Properties of the parallelogram, rectangle, square, rhombus, trapezium and kite

Symmetry about a point, line or plane Recognise line and rotational symmetry Complete shapes with a given axis of symmetry and order of rotational symmetry

Use of Pythagoras’ theorem in 2D and 3D Including its use in any acute–angled triangle where an altitude is given or constructed The angle bisector theorems are excluded

Similarity: areas and volumes of similar figures Understanding how scale factors are related to area and volume

Prove the similarity of two triangles

Congruent shapes

Understand and use SSS, SAS, ASA and RHS conditions to prove the congruence of triangles

Chord, angle and tangent properties of circles To include knowledge of the intersecting chord properties (both internal and external) and the alternate segment theorem

Properties of a cyclic quadrilateral

Loci in two dimensions ‘Tracing paper’ methods will not be acceptable

Constructions of bisector of an angle and of perpendicular bisector (mediator) of a straight line Constructions using only ruler and compasses