S2 Geometry & Trigonometry

Interactive Files & Worksheets for Geometry & Trigonometry

Van Hiele Model of Geometric Thought Mindmap

Van Hiele Model of Geometric Thought Document

The synthetic geometry covered at Leaving Certificate is a continuation of that studied at junior cycle. It is based on Geometry for Post-primary School Mathematics, including terms, definitions, axioms, propositions, theorems, converses and corollaries. The formal underpinning for the system of post-primary geometry is that described by Barry (2001)¹.

At each syllabus level, knowledge of geometrical results from the corresponding syllabus level at Junior Certificate is assumed. It is also envisaged that at all levels students will engage with a dynamic geometry software package.

In particular, at Foundation level and Ordinary level learners should first encounter the geometrical results below through investigation and discovery. Learners are asked to accept these results as true for the purpose of applying them to various contextualised and abstract problems. They should come to appreciate that certain features of shapes or diagrams appear to be independent of the particular examples chosen. These apparently constant features or results can be established in a formal manner through logical proof. Even at the investigative stage, ideas involved in mathematical proof can be developed. Learners should become familiar with the formal proofs of the specified theorems (some of which are examinable at Higher level). Learners will be assessed by means of problems that can be solved using the theory.

1 P.D. Barry. Geometry with Trigonometry, Horwood, Chicester (2001)