- Mathematics Advanced
- Year 11
Plane Geometry
approx. 9 hrs
4 topics
21 concepts
Become competent with Plane Geometry and advance into Year 12 with the right foundations.
approx. 9 hrs
4 topics
21 concepts
Become competent with Plane Geometry and advance into Year 12 with the right foundations.
This learning program covers the essential components of the Year 11 Mathematics Advanced, Plane Geometry topic as outlined the NSW Mathematics syllabus. In Year 11 Plane Geometry, students use congruence and similarity and their application to geometrical proofs and properties of shapes.
This learning program is made up of the following 4 topics, broken down into 21 concepts.
Prove and apply tests for quadrilaterals using similarity results
Apply the intercepts and parallel lines properties to find unknown sides
Solve problems involving similarity ratios and areas and volumes
Apply similar triangle results to solve practical problems
Application of congruent triangles to prove properties of special triangles and quadrilaterals
Choosing a test for congruence (SSS test, SAS test, AAS test, RHS test)
Write formal proofs of congruence of triangles, preserving matching order of vertices
Write formal proofs of similarity of triangles, preserving matching order of vertices
Tests for similar triangles
Prove Pythagoras' theorem using similarity
Converse of Pythagoras' theorem
Apply rule that if two lines are parallel to a third line then they are parallel to one another
Use angle relationships to identify parallel lines
Find angles at a point using angle relationships
Use angle relationships of parallel lines to find the size of unknown angles, giving reasons
Apply Exterior Angle Sum of Polygons
Apply the Interior Angle Sum of a Polygon formula
Investigate and apply the exterior angle of a triangle property to find angles in a given diagram
Investigate and use the angle sum of a triangle property to find angles in a given diagram
Apply the triangle inequality rule
Find unknown sides and angles in a given diagram by using the properties of special triangles and quadrilaterals
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