Mathematics / Year 10 / Measurement and Geometry / Geometric reasoning

Curriculum content descriptions

Formulate proofs involving congruent triangles and angle properties (ACMMG243)

Elaborations
  • 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

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 ...

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: It's what's inside that counts

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

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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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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 ...

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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 ...

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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.

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In a spin

This resource is a web page containing a short task to explore volume of a solid shape. The task involves calculating the volume of the solid formed by rotating a right angled triangle about its hypotenuse A printable resource and solution is also available to support the task. This resource is an activity from the NRICH ...

Video

Stateline: Mapping farmland: using area and trigonometry

In northern Queensland's Gulf region, some farmers use GPS mapping to help manage their extensive properties. Use this clip as a context for applying your understanding of area, in particular your understanding of conversion between square kilometres and hectares. Apply trigonometry and Pythagoras' theorem.

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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 ...

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Trigonometric Ratios

An animated introduction to the basic trigonometric ratios.

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Numeracy wrap: Race across transversals

Interactive activities that guide students to explore angles in parallel lines.

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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.

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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.

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Laptop wrap – a slippery slope

Distance, midpoint and gradient are investigated as students design an Excel spreadsheet and make a Smart Notebook presentation on ski-lifts. Students then contribute to a discussion on the steepest street in the world. 

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Finding Angles From Ratios

An animated tutorial about using a calculator to find an angle when given a trigonometric ratio. An interactive quiz is included.

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Numeracy wrap: Tell me why

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

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ABC News: 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 ...

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Laptop wrap: Talking trigonometry

In this laptop-friendly resource, students consolidate their understanding of trigonometry by investigating practical applications of the ratios, highlighting the process they used to find a solution.

Online

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 ...