Mathematics / Year 10 / Measurement and Geometry / Geometric reasoning

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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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7 direct matches to ACMMG243 | 13 other related resources
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reSolve: Mechanical Linkages: Geometry Proofs

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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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The geometer's warehouse

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

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

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Laptop wrap: Geometry gems

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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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Work sample Year 10 Mathematics: Proof and conjecture

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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

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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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Renovate, Calculate!

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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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reSolve: Trigonometric Trajectories

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In this sequence of two lessons, students investigate trigonometric and Pythagorean relationships through two contexts: researching and building a model zipline ride and outlining a proposal for glider poles. In the first lesson, students apply trigonometric and Pythagorean relationships to investigate the dimensions of ...

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Numeracy wrap: Parallelogram peculiarities

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Interactive activities that guide students to investigate properties of parallelograms.

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Laptop wrap: Talking trigonometry

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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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ABC News: Space debris: the accuracy of space lasers

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

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

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Algebra four

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This is an interactive game for two students in which they solve algebraic equations, similar to 'Connect four'. The players can choose from problems that are one- or two-step, quadratic, have distributive properties or have variables on both sides, and more than one problem type can be chosen. The length of time each player ...

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Factorising Quadratics and Solving - Calculate

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This activity explores the properties of the family of functions and their graphs known as parabolas. The unit includes an AMSI Interactive online module, a range of other AMSI Schools and external links and video tutorials and some extension or enrichment ideas to take their understanding further. A short quiz at the end ...

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

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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 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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Volume and surface area: Year 10 – planning tool

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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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A piece of cake

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In this lesson, students build on their skills in finding volumes and surface areas of prisms and cylinders to design a multi-level celebration cake for a party. They use mathematical modelling to vary the size and shape of the component cakes and to calculate how much frosting is needed.

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Voronoi Diagrams - Calculate

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This unit of work explores coordinate geometry in the context of Voronoi diagrams. Students use linear coordinate geometry to construct Voronoi diagrams by finding the gradient of a line segment, then finding the midpoint, a perpendicular line and finally the perpendicular bisector.

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