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Mathematics / Year 10 / Measurement and Geometry / Geometric reasoning

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

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6 direct matches to ACMMG243 | 14 other related resources
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Online

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

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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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Interactive

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

  • TLF-IDM016261

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

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Interactive

The geometer's warehouse

  • TLF-IDM016684

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.

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Online

reSolve: Mechanical Linkages: Geometry Proofs

  • TLF-IDM021852

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 ...

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Online

Proof: Year 10 – planning tool

  • TLF-IDA003232

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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Text

Work sample Year 10 Mathematics: Proof and conjecture

  • TLF-IDA004066

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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Interactive

Renovate, Calculate!

  • TLF-IDM016724

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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Video

What are pixels?

  • TLF-IDM020591

Meet Kevin Systrom and Piper Hanson as they explain how digital images work. What are pixels, those tiny dots of light, made from? How are colours created and represented? What does Kevin say about the way mathematical functions are used to create different image filters. What is the difference between image resolution ...

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Online

Secondary mathematics: different representations

  • TLF-IDS4971

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 ...

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Online

Secondary mathematics: using real data

  • TLF-IDS4972

These seven learning activities, which focus on the use of 'real data' 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 the three content strands ...

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Text

Round and Round and Round

  • TLF-IDM020739

This resource is a web page containing an interactive that can be used to explore the relationships between the angles of turn that produce the same vertical and horizontal displacements. The task provides an opportunity to apply their understanding of division and recurring decimals. A 'Getting started' page, printable ...

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Online

TIMES Module 22: Measurement and Geometry: introductory trigonometry - teacher guide

  • TLF-IDM008608

This is a 20-page guide for teachers containing an introduction to the three basic trigonometric ratios. A history of trigonometry concludes the module.

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Video

Stateline: Mapping farmland: using area and trigonometry

  • TLF-IDM015626

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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Interactive

Laptop wrap: Talking trigonometry

  • TLF-IDM016176

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.

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In a spin

  • TLF-IDM020741

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 ...

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Tuning and Ratio

  • TLF-IDM020738

This resource is a web page containing a challenging problem solving task that requires an understanding of ratios and logarithms. It explains how intervals such as an octave corresponds to a particular ratio of string lengths which produce the notes. Two types of tuning based on ratios; The Pythagorean Scale and Just Intonation ...

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Video

ABC News: Space debris: the accuracy of space lasers

  • TLF-IDM015754

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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Interactive

Numeracy wrap: Race across transversals

  • TLF-IDM016118

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

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Interactive

Finding Angles From Ratios

  • TLF-IDM016193

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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Interactive

Laptop wrap – a slippery slope

  • TLF-IDM016265

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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