All
• Refine own findings and approaches on the basis of discussions with others
• Identify alternate angles and corresponding angles; understand a proof that:
(i) the sum of the angles of a triangle is 180º and of a quadrilateral is 360º;
(ii) the exterior angle of a triangle is equal to the sum of the two interior opposite angles.
• Solve geometrical problems using side and angle properties of equilateral, isosceles and right-angled triangles and special quadrilaterals, explaining reasoning with diagrams and text; classify quadrilaterals by their geometrical properties
Most
• Review and refine own findings and approaches on the basis of discussions with others
• Record methods, solutions and conclusions
• Explain how to find, calculate and use:
(i) the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons;
(ii) the interior and exterior angles of regular polygons
• Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text
• Know the definition of a circle and the names of its parts; explain why inscribed regular polygons can be constructed by equal divisions of a circle
Some
• Use a range of forms to communicate findings effectively to different audiences
• Distinguish between practical demonstration and proof in a geometrical context
• Investigate Pythagoras’ theorem, using a variety of media, through its historical and cultural roots including ‘picture’ proofs
• Solve multi-step problems using properties of angles, of parallel lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text
• Know that the tangent at any point on a circle is perpendicular to the radius at that point; explain why the perpendicular from the centre to the chord bisects the chord