Mathematics / Year 9 / Measurement and Geometry / Geometric reasoning

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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Work sample Year 9 Mathematics: Similar triangles

This work sample demonstrates evidence of student learning in relation to aspects of the achievement standards for Year 9 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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Work sample Year 9 Mathematics: Cylinder volume

This work sample demonstrates evidence of student learning in relation to aspects of the achievement standards for Year 9 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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Mathematics of bushfire

In these classroom activities students will be introduced to some of the basic mathematical principles that underpin wildfire science, with an emphasis on how theoretical concepts are used to aid our understanding of the real world, and bushfire in particular. They will learn about the complexities of the fire management ...

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Measurement: Foundation to Year 9

This comprehensive resource describes the progression of measurement ideas. The resource demonstrates examples of relevant teaching strategies, investigations, activity plans and connected concepts in measurement including teaching and cultural implications.

Downloadable

Geometry: Foundation to Year 9

This comprehensive resource describes the progression of geometric reasoning. The resource demonstrates examples of relevant teaching strategies, investigations, activity plans and connected concepts in geometry including teaching and cultural implications.

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Graphs: Year 9 – planning tool

This planning resource for Year 9 is for the topic of Graphs. Students work with points, straight lines and line segments on the Cartesian plane, and use the coordinates of points to apply the formulas for calculating the gradient, midpoint and length of a line segment (distance between two points). They use digital tools ...

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Pythagoras and trigonometry (Measurement): Year 9 – planning tool

This planning resource for Year 9 is for the topic of Pythagoras and trigonometry. Students apply and build upon knowledge of Pythagoras’ theorem, angle properties, trigonometry and scales to solve problems involving right-angled triangles.

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Algorithms: Year 9 – planning tool

This planning resource for Year 9 is for the topic of Algorithms. Students draw upon their knowledge of congruency, transformations and ratios of right-angled triangles and apply creativity, critical thinking and reasoning skills to a sequenced geometric problem. For example, students may design a flow chart to prove the ...

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Pythagoras and trigonometry (Space): Year 9 – planning tool

This planning resource for Year 9 is for the topic of Pythagoras and trigonometry. Students develop and use their understanding of the relationship between the corresponding sides of similar right-angled triangles.

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Volume and surface area: cylinders: Year 9 – planning tool

This planning resource for Year 9 is for the topic of Volume and surface area: cylinders. Students calculate the surface area, volume and capacity of cylinders and solve related problems.

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Volume and surface area: prisms: Year 9 – planning tool

This planning resource for Year 9 is for the topic of Volume and surface area: prisms. Students solve problems involving the surface area and volume of right prisms.

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Mathematical modelling (Algebra): Year 9 – planning tool

This planning resource for Year 9 is for the topic of Mathematical modelling. Students use algebraic rules, tables, graphs and digital tools to construct linear and quadratic models for a range of real-life situations, make predictions and solve related problems. They spend time identifying variables to formulate the models ...

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Transformation: Year 9 – planning tool

This planning resource for Year 9 is for the topic of Transformation. Students explore and develop their understanding of the enlargement transformation using dynamic geometry software. They will investigate what changes and what remains the same when a shape or object is enlarged. Students will look for patterns in the ...

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Trigonometry

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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Similarity

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

This is a 24-page guide for teachers. It contains proofs of Pythagoras's theorem and its converse, applications of Pythagoras's theorem and a discussion of Pythagorean triads. A history of Pythagoras's theorem concludes the module.

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

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

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TIMES Module 35: Number and Algebra: proportion - teacher guide

This is a 22-page guide for teachers. The module introduces the idea of direct proportion and illustrates its many uses in science, commerce and measurement. It looks at ratios, gradients and fractions. A history of the development and use of proportion concludes the module.

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

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