Geometry in the plane and proof

Key knowledge
• standard geometric conventions and notation for points, lines and angles, and the definitions of parallel lines, transversals and related angles
• the definitions and properties of common polygons, circles and related geometric constructs
• notions of congruence and similarity and conditions for congruence and similarity, and the sine and cosine rules and conditions for their application
• geometric theorems involving lines, polygons and circles, including Pythagoras’ theorem and its converse.

Key skills
• identify assumptions, give definitions and provide examples and counter-examples using appropriate mathematical language, diagrams and models
• complete geometric constructions using a compass and straight edge and dynamic geometry technology
• model situations and solve problems involving geometry
• prove theorems involving lines, polygons and circles.

Vectors in the plane

Key knowledge
• the standard notation and representations for vectors in the plane, including arrows, coordinates and matrices
• the definition of arithmetical operations for vectors in the plane
• the geometric and coordinate definition of the scalar product of two vectors
• geometrical representation of vectors.

Key skills
• use vectors to model situations involving direction and magnitude
• apply vector operations of scalar multiples, addition, subtraction and scalar product
• use vectors as an alternative geometric tool and apply them to problems in describing position, displacement, velocity and force
• use vectors to solve geometric problems and prove theorems.