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Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning (ACMMG202)
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.
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 ...
This lesson explores the geometry of cutting polygons in different ways and using algebra to express subsequent findings. Students use one straight cut to divide a convex polygon into two new polygons. They make generalisations about the total number of sides of the two new polygons, and about the number of different combinations ...
A 2D Shapes tool that can be used to create geometric objects such as quadrilaterals, circles, triangles, lines, arcs, rays, segments and vectors on a coordinate grid. Plot and label the vertices to reveal the internal angles, side lengths, area and perimeter, then manipulate the shapes on a grid to transform their shape ...
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 activities that guide students to investigate properties of parallelograms.
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.
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 ...
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 ...
Label the three sides of a right-angled triangle as hypotenuse, adjacent and opposite sides. Identify which sides form a trigonometric ratio such as cosine or tangent. Watch a video showing how trigonometry is used to help planes land safely.
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.
An animated tutorial demonstrating planes of symmetry of solids. An interactive quiz is included.
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 ...
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.
This is a Geogebra activity used to teach the area of a parallelogram. Suitable for use with an interactive whiteboard (IWB).
Interactive activities that guide students to explore angles in parallel lines.
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.
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.
This is a 30-page guide for teachers. It contains an introduction to congruence, in particular the congruence tests for triangles. Applications of congruence are included throughout the module.
interactive activities that guide students to explore the interior and exterior angle sums of polygons.