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Listed under:  Mathematics  >  Geometry  >  Transformation (Geometry)  >  Congruence (Geometry)
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Making triangles

In this lesson, students study the concept of triangle inequality, which determines if three positive numbers can serve as the side lengths of a triangle. Students experiment with various combinations of three natural numbers. They investigate whether these numbers can form a triangle and classify and construct the corresponding ...

Online

Shapes and objects: Year 8 – planning tool

This planning resource for Year 8 is for the topic of Shapes and objects. Students begin to explore geometric properties and proof. They identify the properties of quadrilaterals based on transformation, angles, parallel sides, side lengths, diagonals and symmetry.

Online

Proof: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Proof. Students are familiar with the basics of geometry and have been introduced to proof when looking at similar triangles. They will be extending and applying these skills and using deductive reasoning and geometric theorems to solve spatial problems in relation ...

Online

Algorithms: Year 8 – planning tool

This planning resource for Year 8 is for the topic of Algorithms. Students begin to design, create and test algorithms that involve a sequence of steps that identify congruency or similarity of shapes. They describe how algorithms work through classifying and distinguishing between similar and congruent triangles.

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8Sp01A Congruence - Ochre Education

This eight lesson unit of work focuses on congruence. Students explore the congruence of lengths, angles, and shapes, determine the congruence of triangles and shapes using appropriate tests including with algorithms and determine the size of unknown corresponding parts and finally solve problems involving congruence through ...

Online

reSolve: Quarter Cartons

This lesson challenges students to use algebra and proportional reasoning to investigate how changing the size of a paper square or rectangle impacts the dimensions of a box folded from that paper. Students apply knowledge about nets of 3D objects and explore algebraic relationships through a set of hands-on activities ...

Online

reSolve: Mechanical Linkages: Geometry Proofs

This series of six lessons explores geometry proofs using real world contexts focused on the dynamics of linkages and moving joints. Students use physical models and computer simulations, the lessons move from a view of geometry as a study to static diagrams to encompass movement. Each lesson is outlined in detail including ...

Online

reSolve: Polygon Pieces

This lesson explores the geometry of cutting polygons in different ways and using algebra to express subsequent findings. Students use one straight cut to divide a convex polygon into two new polygons. They make generalisations about the total number of sides of the two new polygons, and about the number of different combinations ...

Online

TIMES Module 22: Measurement and Geometry: scale drawings and similarity - teacher guide

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.

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Geometric reasoning - congruence

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 ...

Interactive

Laptop wrap: Geometry gems

A page with a focus on using GeoGebra to enhance student understanding of various geometric properties and the importance of reasoning in proof. A laptop-friendly resource that includes supporting activities and links to resources.

Interactive

The geometer's warehouse

This web-based, multimedia resource focuses on the geometry of the Stage 4 and Stage 5 Mathematics syllabus. It comprises 70 dynamic html worksheets, each exploring a different outcome in Stage 4 and Stage 5 geometry.

Interactive

Numeracy wrap: Parallelogram peculiarities

Interactive activities that guide students to investigate properties of parallelograms.

Online

reSolve: Mechanical Linkages: Quadrilaterals

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 ...