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Develop the conditions for congruence of triangles (ACMMG201)
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This series of six lessons explores geometry using real world contexts focussed on the dynamics of linkages and moving joints of everyday tools and objects. Students use physical models and computer simulations, the lessons move from a view of geometry as a study static diagrams to encompass movement. Each lesson is outlined ...
This is a website designed for both teachers and students that introduces congruence of shapes in the plane through transformations. In particular, transformations, translations, reflections in an axis and rotations of multiples of 90 degrees are used to define congruence and to identify congruent shapes. The four congruence ...
This is a 30-page guide for teachers that explains the central role of construction and presents examples of constructions.
This is a 41-page guide for teachers. It contains an introduction to scale drawings and similarity, and in particular the tests for triangles to be considered similar. Applications of similarity are included throughout the module.
This is a 24-page guide for teachers. It contains proofs of Pythagoras's theorem and its converse, applications of Pythagoras's theorem and a discussion of Pythagorean triads. A history of Pythagoras's theorem concludes the module.
This is a 17-page guide for teachers. It contains the definitions, properties and tests for parallelograms and rectangles. Proofs of the properties and tests are given. Constructions for parallelograms and rectangles are given.
An interactive simulation in which students use Pythagoras' theorem can be used to find distances.
An animated tutorial demonstrating the application of Pythagoras' theorem through some worked examples, followed by a interactive quiz.