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Listed under:  Mathematics  >  Geometry  >  Angles  >  Parallel line angles  >  Corresponding angles
Teacher resource

Primary mathematics: games, simulations and modelling

These seven learning activities, which focus on 'games, simulations and modelling' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use games, ...

Interactive resource

Measures: similar shapes

Compare the sizes and angles of a range of triangles, squares and rectangles. Notice that 'similar shapes' in the mathematical sense have the same shape and possibly different sizes. Corresponding sides are in proportion, and corresponding angles are equal. Identify shapes that are similar and create shapes similar to given ...

Interactive resource

Measures: scaling down

Compare the areas of squares, rectangles and triangles before and after being scaled down (reduced). Notice that 'similar shapes' in the mathematical sense have the same shape but different areas. Explore the relationship between side-length reduction and area reduction when scaling down shapes. This learning object is ...

Interactive resource

Measures: similar solids

Compare the sizes and angles of a range of cubes and rectangular prisms. Notice that 'similar solids' in the mathematical sense have the same shape and possibly different sizes. Corresponding sides are in proportion, and corresponding angles are equal. Identify solids that are similar, and create solids similar to given ...

Interactive resource

Measures: scaling up solids

Compare the volumes of cubes and rectangular prisms before and after being scaled up (enlarged). Notice that 'similar solids' in the mathematical sense have the same shape but different volumes. Explore the relationship between side length and volume when scaling up solids. This learning object is the fifth in a series ...

Interactive resource

Measures: scaling down solids

Compare the volumes of cubes and rectangular prisms before and after being scaled down (reduced). Notice that 'similar solids' in the mathematical sense have the same shape but different volumes. Explore the relationship between side length and volume when scaling down solids. This learning object is the sixth in a series ...

Interactive resource

Measures: volumes

Compare the volumes of a range of rectangular prisms when scaling up (enlarging) side lengths by different ratios. Notice that the rectangular prisms are not similar in the mathematical sense, but it is possible to predict the effect on the volume produced by the scaling of the sides. Identify and describe the relationship ...

Interactive resource

Trigonometry: measuring with triangles

Compare the shadows cast by a small stick and a larger object such as a column of a Greek building. Check the angles at which the shadows are cast and confirm whether the two objects create similar triangles. Use equivalent ratios to calculate the lengths of a triangle's sides: the height of an object or the length of a ...

Interactive resource

Trigonometry: similar triangles

Examine pairs of right-angled triangles. Check that each pair of triangles is similar by identifying all three pairs of corresponding angles. Label corresponding angles with matching symbols. This learning object is one in a series of ten objects.

Interactive resource

Trigonometry: sine

Look at an explanation of the trigonometric ratios: sine, cosine and tangent. Adjust the angles of a right-angled triangle within a unit circle (radius of one unit). Find corresponding sides in similar triangles and find relationships between ratios. Identify the sine ratio and enter the sine values of angles from 0–90 ...

Interactive resource

Trigonometry: using tangent

Solve measurement problems involving right-angled triangles by using similar triangles and trigonometric methods, including tangent values. Identify corresponding sides and ratio relationships in similar triangles. Solve measurement problems by using tangent values to calculate side lengths in triangles. For example, find ...

Interactive resource

Trigonometry: using sine

Solve measurement problems involving right-angled triangles by using similar triangles and trigonometric methods, including sine values. Identify corresponding sides and ratio relationships in similar triangles. Solve measurement problems by using sine values to calculate side lengths in triangles. For example, find the ...

Interactive resource

Trigonometry: finding the hypotenuse

Solve measurement problems involving right-angled triangles by using similar triangles and trigonometric methods, including sine values. Identify corresponding sides and ratio relationships in similar triangles. Solve measurement problems by using sine values to calculate the length of a hypotenuse in triangles. For example, ...

Interactive resource

Exploring relationships of angles

Explore angles formed by a transversal line intersecting parallel lines. Look at illustrations showing pairs of angles: vertically opposite, corresponding and alternate angles. Name pairs of angles to score points and help a monkey drive to the supermarket to buy food.

Teacher resource

TIMES Module 9: Measurement and Geometry: introduction to plane geometry - teacher guide

This is a 16-page guide for teachers. It provides an introduction to the initial ideas of plane geometry. Points and lines are introduced as fundamental objects in the study of geometry. Angles and parallelism are the initial areas of attention in a more formal approach to geometry that occurs from year 7.

Teacher resource

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

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.

Teacher resource

TIMES Module 21: Measurement and Geometry: rhombuses, kites and trapezia - teacher guide

This is a 32-page guide for teachers. It contains the definitions, properties and tests for rhombuses, kites and trapezia. Proofs of the properties and tests are given. Constructions for rhombuses, kites and trapezia are provided.

Teacher resource

TIMES Module 26: Measurement and Geometry: circle geometry - teacher guide

This is a 44-page guide for teachers. It contains theorems on chords, arcs, angles and secants associated with circles.

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 ...

Teacher resource

Geometric reasoning including parallel lines and angle sum of a triangle

This is a website designed for both teachers and students that addresses geometry from the Australian Curriculum for year 9 students. It contains material on geometry and includes information regarding parallel lines and the angle sum of triangles. There are pages for both teachers and students. The student pages contain ...