Mathematics / Year 10 / Measurement and Geometry / Geometric reasoning

Curriculum content descriptions

Formulate proofs involving congruent triangles and angle properties (ACMMG243)

  • applying an understanding of relationships to deduce properties of geometric figures (for example the base angles of an isosceles triangle are equal)
General capabilities
  • Numeracy Numeracy
ScOT terms

Angles,  Congruence (Geometry),  Triangles (Shapes),  Mathematical proofs


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 ...


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.


Numeracy wrap: It's what's inside that counts

interactive activities that guide students to explore the interior and exterior angle sums of polygons.


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.


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 ...


Work sample Year 10 Mathematics: Proof and conjecture

This work sample demonstrates evidence of student learning in relation to aspects of the achievement standards for Year 10 Mathematics. The primary purpose for the work sample is to demonstrate the standard, so the focus is on what is evident in the sample not how it was created. The sample is an authentic representation ...


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.


Pythagoras and trigonometry: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Pythagoras and trigonometry. Students apply their knowledge of Pythagoras' theorem to solve problems involving angles of elevation and depression and direction. They explore how direction can be indicated using true bearings and compass points.


Volume and surface area: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Volume and surface area. Students extend their application of volume and surface area to solve problems on composite solids. Students will need to be able to visualise the individual elements of the composite solids and identify the areas where these elements touch.


Numeracy wrap: Parallelogram peculiarities

Interactive activities that guide students to investigate properties of parallelograms.


Laptop wrap: Parallelendicular

Students construct a series of GeoGebra applets that investigate the parameters gradient and intercepts of straight lines. They reinforce this knowledge with Microsoft Math 3.0. 


Numeracy wrap: Tell me why

Interactive activities that guide students to consider the use and presentation of geometric reasoning.


Laptop wrap: Under the surface

In this laptop-friendly resource, students consider the difference between volume and surface area before posing practical problems. They then consider issues relating to unit conversions and similar figures.


Catalyst: Applying trigonometry: leaning tower

The Leaning Tower of Gingin is the centrepiece of the Gravity Discovery Centre. The Catalyst team of Derek, Simon and Anja drop watermelons from the tower, to examine the rate at which they fall. They are testing Galileo's theory about falling objects. The dimensions of the tower provide an opportunity to apply some basic ...


The Mathematical Toolkit

A 2D Shapes tool that can be used to create geometric objects such as quadrilaterals, circles, triangles, lines, arcs, rays, segments and vectors on a coordinate grid. Plot and label the vertices to reveal the internal angles, side lengths, area and perimeter, then manipulate the shapes on a grid to transform their shape ...


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.


The Numberline

An interactive tool that can help students explore a number line, including points representing integers, fractions and decimals


Trigonometric Ratios

An animated introduction to the basic trigonometric ratios.


TIMES Module 24: Measurement and Geometry: further trigonometry - teacher guide

This is a 32-page guide for teachers. It provides an introduction to the sine rule and cosine rule and their applications.


Secondary mathematics: different representations

These seven learning activities, which focus on 'representations' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use different representations ...