Mathematics / Year 9 / Measurement and Geometry / Geometric reasoning

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

Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar (ACMMG220)

Elaborations
  • establishing the conditions for similarity of two triangles and comparing this to the conditions for congruence
  • using the properties of similarity and ratio, and correct mathematical notation and language, to solve problems involving enlargement (for example, scale diagrams)
  • using the enlargement transformation to establish similarity, understanding that similarity and congruence help describe relationships between geometrical shapes and are important elements of reasoning and proof
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
ScOT terms

Dilation,  Triangles (Shapes),  Similarity (Geometry)

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reSolve: Mechanical Linkages: Similar Triangles

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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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Similarity

  • TLF-IDM013359

This is a website designed for both teachers and students, which addresses similarity from the Australian Curriculum for year 9 students. It contains material on enlargement transformation and similar triangles. There are pages for both teachers and students. The student pages contain interactive questions for students ...

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Trigonometry

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This is a website designed for both teachers and students, which addresses content on trigonometry from the Australian Curriculum for year 9 students. It contains material on working with the similarity of right-angled triangles, the three basic trigonometric ratios, and solving problems with trigonometry. There are pages ...

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Volume of a Pyramid and a Cone

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This resource is a web page containing an investigative task to explore volume. Derive the formulae for the volumes of a square-based pyramid and a cone, using mathematical concepts. A printable resource is also available to support the task. This resource is an activity from the NRICH website.

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reSolve: Tree Biomass

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In this sequence of two lessons, students investigate how many trees would be required to supply paper for their school for a year. Students use similar triangles, Pythagoras' Theorem and algebra to design and construct a Biltmore stick, used to measure the diameter and height of a tree. They measure trees, calculate their ...

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reSolve: Gradient and Tangent

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This sequence of two lessons investigates gradient and angle by applying the tangent ratio to find the angles represented by a road sign or the angle of a street. In the first lesson, students research what a road grade is and determine the actual angle of a road given its grade. They then construct their own road sign ...

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TIMES Module 20: Measurement and Geometry: parallelograms and rectangles - teacher guide

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This is a 17-page guide for teachers. It contains the definitions, properties and tests for parallelograms and rectangles. Proofs of the properties and tests are given. Constructions for parallelograms and rectangles are given.

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TIMES Module 15: Measurement and Geometry: Pythagoras's theorem - teacher guide

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

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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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reSolve: Pythagoras' Theorem - Phone finding

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This lesson challenges students to apply Pythagoras' Theorem to explore a practical real-world problem. Students explore technology reliant on mathematical concepts. The lesson is outlined in detail including curriculum links, vocabulary, materials needed, sample answers, discussion points and student resources such as ...

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