AC9M8M06 Year 8 Mathematics

Content descriptor use Pythagoras’ theorem to solve problems involving the side lengths of right-angled triangles

Elaborations

• • Elaboration discussing and comparing different applications, demonstrations and proofs of Pythagoras’ theorem, from Egypt and Mesopotamia, Greece, India and China with other historical and contemporary applications and proofs
• • Elaboration using Pythagoras’ theorem to determine unknown lengths of sides in right-angled triangles and finding lengths of sides of right-angled triangles in practical applications
• • Elaboration recognising the relationship between the squares of lengths of sides for different types of triangles: right-angled, acute or obtuse
• • Elaboration identifying Pythagorean triples, such as (3,4,5), (5,12,13), (7, 24, 25) and (8,15, 17)
• • Elaboration investigating how Pythagoras' theorem can be applied to determine the distance between two points in the plane, and how this can be used by predictive algorithms to navigate autonomous vehicles