Mathematics / Year 10 / Measurement and Geometry / Geometric reasoning

Version 8
View on Australian Curriculum website Australian Curriculum, Assessment and Reporting Authority
Curriculum content descriptions

Prove and apply angle and chord properties of circles (ACMMG272)

Elaborations
  • performing a sequence of steps to determine an unknown angle or length in a diagram involving a circle, or circles, giving a justification in moving from one step to the next
  • communicating a proof using a logical sequence of statements
  • proving results involving chords of circles
General capabilities
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Angles,  Mathematical proofs,  Chords (Lines)

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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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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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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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Online

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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Online

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

  • TLF-IDM008829

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

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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

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

Numeracy wrap: Tell me why

  • TLF-IDM016554

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

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Interactive

Trigonometric Ratios

  • TLF-IDM016660

An animated introduction to the basic trigonometric ratios.

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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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Interactive

Numeracy wrap: Race across transversals

  • TLF-IDM016118

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

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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

Laptop wrap: Parallelendicular

  • TLF-IDM016249

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. 

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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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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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