Mathematics / Year 7 / Measurement and Geometry / Geometric reasoning

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

Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral (ACMMG166)

Elaborations
  • using concrete materials and digital technologies to investigate the angle sum of a triangle and quadrilateral
General capabilities
  • Numeracy Numeracy
ScOT terms

Polygons,  Adjacent angles

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Year level 7-8
Resource type
Learning area Mathematics
Interactive resource

Exploring quadrilaterals

Examine the sides and angles of a four-sided shape. Identify its geometric properties such as the number of sides of equal length. Classify the shape as a parallelogram, rhombus, square, rectangle, kite or trapezium. Notice that some quadrilaterals can be classified in different ways.

Interactive resource

Exploring angles

Resize a triangle by moving its vertices. Notice that the sum of the three interior angles is always 180 degrees. Watch a video showing how angles are used in designing and riding bicycles.

Interactive Resource

The geometer's warehouse

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.

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 ...

Interactive Resource

Numeracy wrap: Tell me why

Interactive activities that guide students to consider the use and presentation of geometric reasoning.

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

Exploring area and perimeter

Build a compound shape on a grid from shapes such as rectangles, semicircles and squares. Notice that the total area of the compound shape equals the sum of the areas of all of the component shapes. Build a rectangle to produce a given area and perimeter. Identify shapes used to form a compound shape. Calculate the area ...

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 ...

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BBC Bitesize: angles - revision

This set of illustrated information sheets summarises facts related to angle types, measuring and estimating the size of angles, and the angle sum of triangles and quadrilaterals. Students are given the opportunity to try examples. Worked solutions are available. This resource is one of a series of online resources from ...

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 ...

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 ...

Interactive resource

Exploring transformations

Explore transformations of shapes such as rotation, translation or reflection. Identify which transformations have been applied to circles and polygons to produce new images. For example, the original image may have been rotated 90 degrees around the point (0,0). Notice how the coordinates of the transformed image are related ...

Interactive Resource

Renovate, Calculate!

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.

Moving Image

Area of composite shapes

Finding the area of a rectangle is quite easy. But what if the shape you're working with is not a simple rectangle? What if it's a composite shape made up of two different-sized rectangles? See how to work out the area, and discover why you need to use the same units.

Interactive resource

Exploring ratios and proportions

Explore ratios by comparing the dimensions of two rectangles. Choose a scale to enlarge the smaller shape and identify whether its sides are proportional to those of the larger rectangle. For example, a rectangle with sides in the ratio 4:5 has an equivalent ratio to a rectangle with sides in the ratio 12:15. Watch a video ...

Moving Image

Working out the areas

Do you know how to work out the area of a square, a rectangle or a triangle? Learn the simple maths formulas needed from this video. What would be the area of a rectangle with a height of 5cm and a length of 3cm?

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BBC Bitesize: 2-D shapes - revision

This is a collection of information sheets on the geometrical properties of special quadrilaterals and 2-D representations of 3-D shapes. Students have access to a multiple-choice test to assess their knowledge of quadrilaterals and representations of 3-D shapes. This resource is one of a series of online resources from ...

Moving Image

Area of a square and a triangle

Do you know the formula for working out the area of a square? How about a triangle? Watch this short maths video to learn the formulas for both.