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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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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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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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Online

Pythagoras and trigonometry: Year 10 – planning tool

  • TLF-IDA003236

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.

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Volume and surface area: Year 10 – planning tool

  • TLF-IDA003238

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.

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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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Online

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

  • TLF-IDM009166

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

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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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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TIMES Module 34: Number and Algebra: quadratic equations - teacher guide

  • TLF-IDM009038

This is a 19-page guide for teachers. It introduces quadratic equations and methods for solving them.

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TIMES Module 25: Measurement and Geometry: trigonometric functions - teacher guide

  • TLF-IDM009049

This is a 21-page guide for teachers. It provides an introduction to the sine, cosine and tangent functions and applications of these.

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TIMES Module 29: Number and Algebra: introduction to coordinate geometry - teacher guide

  • TLF-IDM009164

This is a 22-page guide for teachers. This module introduces coordinate geometry. The introduction includes finding the distance between two points, finding the coordinates of the midpoint between two points, determining the gradient of a line and determining the equation of a line.

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Interactive

Laptop wrap: Geometry gems

  • TLF-IDM016150

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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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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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

Numeracy wrap: Parallelogram peculiarities

  • TLF-IDM016264

Interactive activities that guide students to investigate properties of parallelograms.

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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

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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Video

Catalyst: Applying trigonometry: leaning tower

  • TLF-IDM015448

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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