AC9M10SP01 Year 10 Mathematics

This Content Descriptor from Year 10 Mathematics provides the specific knowledge and skills students should learn. Use it to plan lessons, create learning sequences, and design assessments that align with the Australian Curriculum v9.

apply deductive reasoning to proofs involving shapes in the plane and use theorems to solve spatial problems

Elaborations

• 1 distinguishing between a practical demonstration and a proof; for example, demonstrating that triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent
• 2 developing proofs involving congruent triangles and angle properties, communicating the proof using a sequence of logically connected statements
• 3 applying an understanding of relationships to deduce properties of geometric figures; for example, the base angles of an isosceles triangle are equal
• 4 investigating proofs of geometric theorems and using them to solve spatial problems; for example, applying logical reasoning and similarity to proofs and numerical exercises involving plane shapes; using visual proofs to justify solutions
• 5 using dynamic geometric software to investigate the shortest path that touches 3 sides of a rectangle, starting and finishing at the same point and proving that the path forms a parallelogram
• 6 investigating how automated theorem provers (ATP) and interactive proof assistants (IPA) allow mathematicians and artificial intelligence systems to work collaboratively to construct or test formal proofs

Related Achievement Standards