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Geometric reasoning

Geometric reasoning is the use of critical thinking, logical argument and spatial reasoning to solve problems and find new relationships. Students must first have a critical understanding of any underlying assumptions and relationships. This allows them to develop coherent knowledge and apply their reasoning skills.

The purpose of geometric reasoning is to determine results from previously established truths and to then apply these results in the solution of problems. It can also be used to verify or prove results.

Big ideas

By actively exploring shapes and their properties, students can discover inter-relationships which helps to organise their understanding of geometric ideas.


Students may encounter misunderstandings and difficulties which hinder further development of their geometric knowledge.

Good teaching

Good teaching of geometry enables students to visualise spatial relationships, recognise connections, make conclusions and communicate results.


Assessment can serve a number of purposes. Effective teaching is maximised when a variety of types is used.


Student activities that appear in other parts of the drawer have been collected here.


All downloadable files, such as student worksheets, solutions, slideshow presentations, quizzes, information sheets, are available here.


The Geometric Reasoning drawer was written by a team from the Mathematical Association of New South Wales led by Nikky Vanderhout, Professional Learning Consultant.