Mathematics / Year 7 / Measurement and Geometry / Geometric reasoning

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

Classify triangles according to their side and angle properties and describe quadrilaterals (ACMMG165)

Elaborations
  • identifying side and angle properties of scalene, isosceles, right-angled and obtuse-angled triangles
  • describing squares, rectangles, rhombuses, parallelograms, kites and trapeziums
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
ScOT terms

Angles,  Triangles (Shapes),  Sides (Polygons)

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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.

Moving Image

Types of triangles

What is the difference between equilateral, isosceles and scalene triangles? See if you can find and classify triangles based on the definitions given in this maths video.

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.

Teacher resource

reSolve: Mechanical Linkages: Angles and Lines

This sequence of lessons explores the geometry of angles using real world contexts including the dynamics of folding and joints. Students investigate side lengths and angles, supported by using physical models and computer simulation. There are opportunities to develop geometric language and to highlight how mathematical ...

Text

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

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

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

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

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.

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

HOTmaths: exploring kites

Use a tool to explore and identify the properties of kites. For example, investigate angles, side lengths and the lengths of diagonals in kites.

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

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. ...

Moving Image

The amazing 'angle-a-tron'

Lost your protractor? Well, find out how to make an 'angle-a-tron'. This might just be the coolest mathematical tool you've ever used. Measure all sorts of angles. It's easy with an angle-a-tron!

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.

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

Exploring the Pythagorean theorem

Adjust the dimensions of a right-angled triangle. Calculate the area of squares bordering each side of the triangle. Notice that the area of the square bordering the hypotenuse is equal to the sum of the areas of the squares bordering the other two sides. Watch a video showing how Pythagoras's theorem is used to determine ...

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.

Interactive Resource

Numeracy wrap: Race across transversals

Interactive activities that guide students to explore angles in parallel lines.