# Mathematics / Year 10 / Space

Version 9
Curriculum content descriptions

apply deductive reasoning to proofs involving shapes in the plane and use theorems to solve spatial problems (AC9M10SP01)

Elaborations
• 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
• developing proofs involving congruent triangles and angle properties, communicating the proof using a sequence of logically connected statements
• applying an understanding of relationships to deduce properties of geometric figures; for example, the base angles of an isosceles triangle are equal
• 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
• 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
General capabilities
• Critical and creative thinking Critical and Creative Thinking
ScOT terms

Theorems,  Visual proofs,  Geometry,  Deductive reasoning

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