Objectives:


Support:

  • Distinguish between conventions, definitions and derived properties.
  • Identify alternate angles and corresponding angles;
  • understand a proof that:
    • the sum of the angles of a triangle is 180° and of a quadrilateral is 360°;
    • 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 geometric properties.
  • Use straight edge and compasses to construct:
    • the mid-point and perpendicular bisector of a line segment;
    • the bisector of an angle;
    • the perpendicular from a point to a line;
    • the perpendicular from a point on a line;
    • a triangle, given three sides (SSS);
    • use ICT to explore these constructions.
  • Understand congruence.

Core:

  • Distinguish between conventions, definitions and derived properties, practical demonstration and proof; know underlying assumptions, recognising their importance and limitations, and the effect of varying them.
  • Explain how to find, calculate and use:
    • the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons,
    • 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.
  • Use straight edge and compasses to construct a triangle, given right angle, hypotenuse and side (RHS); use ICT to explore constructions of triangles and other 2-D shapes.
  • Apply the conditions SSS, SAS, ASA or RHS to establish the congruence of triangles.
  • Know that if two 2-D shapes are similar, corresponding angles are equal and corresponding sides are in the same ratio.
  • Find the locus of a point that moves according to a simple rule, both by reasoning and by using ICT.
  • Explore connections in mathematics across a range of contexts: shape and space.

Extension:

  • Understand and apply Pythagoras’ theorem.
  • 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.
  • Know from experience of constructing them that triangles given SSS, SAS, ASA or RHS are unique, but that triangles given SSA or AAA are not.
  • Find the locus of a point that moves according to a more complex rule, involving loci and simple constructions.

Key Vocabulary:

  • polygons, interior / exterior angles, regular, parallel, intersecting, circumference, radius, diameter, chord, tangent, segment, scale, construction (SSS, SAS, ASA, SSA, AAA, RHS), hypotenuse, right-angle, equilateral, isosceles, scalene, perpendicular bisector, loci, Pythagoras, hypotenuse, similar.

Suggested Lesson Outcomes:


SUPPORT TARGET CORE

Framework:










Teaching & Learning Resources:


Angle Rules Resources
Circles Resources
Triangle Resources
Proof Resources
Construction Resources
Loci Resources
Pythagoras Resources