solve spatial problems, applying angle properties, scale, similarity, ratio, Pythagoras’ theorem and trigonometry in right-angled triangles
Elaborations
investigating the applications of Pythagoras’ theorem in authentic problems, including applying Pythagoras’ theorem and trigonometry to problems in surveying and design
applying the formula for calculation of distances between points on the Cartesian plane from their coordinates, emphasising the connection to vertical and horizontal displacements between the points
understanding the relationship between the corresponding sides of similar right-angled triangles and establishing the relationship between areas of similar figures and the ratio of corresponding sides, the scale factor
using images of proportional relationships to estimate actual measurements (for example, taking a photograph of a person standing in front of a tree and using the image and scale to estimate the height of the tree), discussing the findings and ways to improve the estimates
investigating theorems and conjectures involving triangles, for example, the triangle inequality and generalising links between the Pythagorean rule for right-angled triangles, and related inequalities for acute and obtuse triangles, determining the minimal sets of information for a triangle from which other measures can all be determined
using knowledge of similar triangles, Pythagoras’ theorem, rates and algebra to design and construct a Biltmore stick, used to measure the diameter and height of a tree, and calculating the density and dry mass to predict how much paper could be manufactured from the tree
Code
VC2M9M03
Curriculum resources and support
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