Close message Scootle will stop supporting resources that use the Adobe Flash plug-in from 18 Dec 2020. Learning paths that include these resources will have alerts to notify teachers and students that one or more of the resources will be unavailable. Click here for more info.

Mathematics / Year 10 / Measurement and Geometry / Geometric reasoning

View on Australian Curriculum website Australian Curriculum, Assessment and Reporting Authority
Curriculum content descriptions

Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes (ACMMG244)

Elaborations
  • distinguishing between a practical demonstration and a proof (for example demonstrating triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent)
  • performing a sequence of steps to determine an unknown angle giving a justification in moving from one step to the next.
  • communicating a proof using a sequence of logically connected statements
General capabilities
  • Numeracy Numeracy
ScOT terms

Shapes (Geometry),  Reasoning,  Congruence (Geometry),  Mathematical proofs,  Similarity (Geometry)

Interactive Resource

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.

Teacher resource

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.

Teacher resource

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 ...

Interactive Resource

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 resource

Congruent triangles

Find out about congruent and non-congruent triangles and the conditions required to make them. Use line segments and angles to build two congruent triangles for three different combinations of sides and angles. Explore the SSS case (side, side, side), the SAS case (two sides and the included angle) and the ASA case (two ...

Interactive Resource

Gapminder world

This is an interactive resource featuring an animated scatter plot displaying the development of over 200 countries between 1800 and 2011 based on data for two variables, the default being income per person and life expectancy, with population size represented by the size of the plotted points (bubbles). The graph has a ...

Teacher resource

Australia's Trade through Time

Using an interactive timeline created by the Department of Foreign Affairs and Trade, this Teacher guide provides 12 series of learning experiences that engage students in the analysis and interpretation of data about Australian trade from 1900 to the present day. Students study videos, tables, images and texts in order ...

Moving Image

Why borrowing can cost you more

Think credit cards are basically free money? Gen Fricker will make you think again. Learn how interest rates and fees affect the money you borrow, and why they may be more expensive in the long run. Oh dear! Then test yourself with ASIC MoneySmart's "Things to think about" classroom exercises.  

Teacher resource

Trade and Investment at a Glance

Using an illustrated report from the Department of Foreign Affairs and Trade, this Teacher guide provides ten learning sequences that engage students in the analysis and interpretation of data about Australian imports and exports. Students: identify Australia's major exports and imports; investigate international trade ...

Assessment resource

Trigonometry: assessment

Test your understanding of angles and their sine, cosine and tangent values. Use a unit circle tool to find sine, cosine and tangent values in different quadrants. Use the tool to find the angle when given sine, cosine or tangent values. Determine the values for angles between 0° and 360°. Solve problems by using the unit ...

Moving Image

What is opportunity cost?

What is the true cost of buying something? Gen Fricker explains that it's more than just money. Learn about opportunity cost - what it is, why it's a helpful tool and when to use it. Simple! Then test yourself with ASIC MoneySmart's "Things to think about" classroom exercises.  

Teacher resource

Turn up the volume - unit of work

In this unit of work students explore and explain the connections between the surface area and volume of different shapes and how each attribute is measured.

Teacher resource

Teacher's guide: global development quiz

This is a teacher resource with a downloadable guide describing a number of quizzes based on Gapminder world for use with a computer and projector in a whole-class situation. Each quiz is based on an animated scatter plot and requires students to compare the development of countries between 1800 and 2011 based on data for ...

Teacher resource

reSolve: Trigonometric Trajectories

In this sequence of two lessons, students investigate trigonometric and Pythagorean relationships through two contexts: researching and building a model zipline ride and outlining a proposal for glider poles. In the first lesson, students apply trigonometric and Pythagorean relationships to investigate the dimensions of ...

Interactive Resource

Renovate, Calculate!

A student resource that explores the use of mathematics in the trades. Highly interactive investigations into ratio, areas of special quadrilaterals and right-angled trigonometry.

Teacher resource

Top drawer teachers

This is a website that covers five mathematical topics: fractions, mental computation, patterns, statistical literacy and ‘reasoning’. It also explores good teaching practice linked to classroom activities including how to address common misunderstandings. There is also a section for assessment, as well as worksheets with ...

Interactive resource

Trig degrees

Use a unit circle tool to explore sine, cosine and tangent values in different quadrants. Determine the values for angles between 0° and 360°. Observe the symmetry and patterns of the functions to predict the behaviour of the graphs and the values for the functions in different quadrants. Observe the graphs animate and ...

Teacher resource

Teacher's guide: 200 years that changed the world

This is a teacher resource explaining how to use an animated scatter plot from Gapminder world in the context of a presentation to students about global development over the past 200 years. The resource consists of a step-by-step guide to making effective use of the scatter plot, which represents the development in wealth ...

Moving Image

Space debris: the accuracy of space lasers

In space there are thousands of human-made objects (satellites and space junk) orbiting Earth. To avoid collision with space debris, satellites are manoeuvred out of its path. Discover how space debris is tracked using lasers, and about accuracy's effects on the lifetime of the satellite. Find out, using trigonometry, the ...

Dataset

Data in Gapminder world

This resource is a dataset providing data for a number of indicators of development over time for more than 200 countries. The indicators fall into the following categories: population, health, economy, environment, work, infrastructure, energy and education, with over 500 sets of data in total. Each set of data can be ...