AC9M9M03

Elaborations

• AC9M9M03_E1investigating the applications of Pythagoras’ theorem in authentic problems, including applying Pythagoras’ theorem and trigonometry to problems in surveying and design
• AC9M9M03_E2applying 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
• AC9M9M03_E3understanding 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
• AC9M9M03_E4using 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
• AC9M9M03_E5investigating 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
• AC9M9M03_E6using 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
• AC9M9M03_E7investigating how autonomous vehicles solve spatial problems using algorithms based on geometric properties relating to angles, distances and scale