AC9M10SP01

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

Elaborations

AC9M10SP01_E1 - 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
AC9M10SP01_E2 - developing proofs involving congruent triangles and angle properties, communicating the proof using a sequence of logically connected statements
AC9M10SP01_E3 - applying an understanding of relationships to deduce properties of geometric figures; for example, the base angles of an isosceles triangle are equal
AC9M10SP01_E4 - 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
AC9M10SP01_E5 - 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

Achievement Standard Components

ASMAT1010 - They use deductive reasoning, theorems and algorithms to solve  spatial problems.