Mathematics / Year 8 / Measurement and Geometry / Geometric reasoning

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Curriculum content descriptions

Develop the conditions for congruence of triangles (ACMMG201)

Elaborations
  • investigating the minimal conditions needed for the unique construction of triangles, leading to the establishment of the conditions for congruence (SSS, SAS, ASA and RHS)
  • solving problems using the properties of congruent figures
  • constructing triangles using the conditions for congruence
General capabilities
  • Numeracy Numeracy
ScOT terms

Congruence (Geometry),  Triangles (Shapes)

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Year level 7-8
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Learning area Mathematics
Text

Geometric reasoning - congruence

This is a website designed for both teachers and students that introduces congruence of shapes in the plane through transformations. In particular, transformations, translations, reflections in an axis and rotations of multiples of 90 degrees are used to define congruence and to identify congruent shapes. The four congruence ...

Teacher resource

reSolve: Mechanical Linkages: Quadrilaterals

This series of six lessons explores geometry using real world contexts focussed on the dynamics of linkages and moving joints of everyday tools and objects. Students use physical models and computer simulations, the lessons move from a view of geometry as a study static diagrams to encompass movement. Each lesson is outlined ...

Interactive resource

Congruent triangles

Find out about congruent and non-congruent triangles and the conditions required to make them. Use line segments and angles to build two congruent triangles for three different combinations of sides and angles. Explore the SSS case (side, side, side), the SAS case (two sides and the included angle) and the ASA case (two ...

Interactive resource

Area of triangles

Find the area of different types of triangles on a grid. Explore how the formula works. First, estimate the area of a chosen triangle on a grid. Next, work out the correct formula by assembling a series of triangles and rectangles. Then, compare the actual area of the triangle with your original estimate. Practise applying ...

Assessment resource

Area of triangles: assessment

Test your understanding of how to use the formula for calculating the area of triangles. Find the area of nine different triangles on a grid. First, predict the area of a chosen triangle on a grid. Find the base and height measurements of the triangle using an animation. Then, substitute the base and height measurements ...

Interactive resource

Exploring triangles

Find an active triangle in a photograph. Work out its angles by applying principles of opposite angles, complementary angles, supplementary angles and the sum of interior angles. Watch a video showing how triangles are used in buildings and other structures.

Interactive Resource

Planes of Symmetry

An animated tutorial demonstrating planes of symmetry of solids. An interactive quiz is included.

Image

Symmetry and pattern: the art of oriental carpets

This resource is a website about the study of symmetry through analysing patterns in oriental carpets. It presents a gallery of different oriental rugs. Details about the patterns in each rug can be accessed by selecting the image of the rug or the key below the images. There are links to pages that explain symmetry and ...

Moving Image

Mapping farmland: using area and trigonometry

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.

Interactive Resource

Pythagoras' Theorem

An animated introduction to Pythagoras' theorem followed by an interactive quiz.

Interactive Resource

Using Pythagoras' Theorem

An animated introduction to the use of Pythagoras' theorem followed by an interactive quiz.

Interactive resource

Area of triangles: triangles without vertical or horizontal sides

Find the area of triangles that do not have vertical or horizontal sides. Explore how the formula works. First, estimate the area of a chosen triangle on a grid. Next, work out the correct formula by assembling a series of triangles and rectangles. Then, compare the actual area of the triangle with your original estimate. ...

Interactive resource

Area of triangles: height intersects with the base outside the triangle

Find the area of triangles with vertical or horizontal sides. In this type of triangle, the base may be chosen so that the height intersects with the base outside the triangle. Explore how the formula for finding the area of a triangle works. First, estimate the area of a chosen triangle on a grid. Next, work out the correct ...

Moving Image

Mystery man Pythagoras meets his match

What do you know about Pythagoras? Join Vi Hart as she not only explains his theorem but raises some legends about his dark past! Follow Vi's timeline of famous mathematicians to find out in which century Pythagoras lived. See how Vi shows a proof of his theorem and raises what was a big dilemma for Pythagoras: the irrational ...

Text

BBC Bitesize: transformations - revision

This is a set of illustrated information sheets with a focus on congruence and transformations. Examples with answers are included and students have access to multiple-choice questions to assess their learning. This resource is one of a series of online resources from the BBC's Bitesize collection.

Interactive resource

Area of triangles: height intersects with the base inside the triangle

Find the area of triangles that have vertical or horizontal sides. In this type of triangle, the height intersects with the base inside the triangle. Explore how the formula for finding the area of a triangle works. First, estimate the area of a chosen triangle on a grid. Next, work out the correct formula by assembling ...

MovingImage

Using Pythagoras' Theorem (Simulation)

An interactive simulation in which students use Pythagoras' theorem can be used to find distances.

Interactive Resource

Examples of Pythagoras' Theorem Part 1

An animated tutorial demonstrating the application of Pythagoras' theorem through some worked examples, followed by a interactive quiz.

Interactive Resource

Examples of Pythagoras' Theorem Part 2

An animated tutorial demonstrating the application of Pythagoras' theorem through some worked examples, followed by a interactive quiz.

Teacher resource

Starting Smart: how are shapes and objects related?

This curriculum resource package is a ten-week middle years teaching plan and set of supporting resources to extend students' understanding of geometrical language and spatial relationships. Students use concrete materials and interactive geometry software packages to compare and describe geometrical attributes and investigate ...