• Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes.
  • Identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle, and recognise vertically opposite angles.
  • Use angle measure; distinguish between and estimate the size of acute, obtuse and reflex angles.
  • Use a ruler and protractor to:
    • measure and draw lines to the nearest millimetre and angles, including reflex angles, to the nearest degree;
    • construct a triangle given two sides and the included angle (SAS) or two angles and the included side (ASA).


  • 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
  • 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.
  • Investigate in a range of contexts: shape and space.


  • 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.
  • Know the definition of a circle and the names of its parts.
  • Use straight edge and compasses to construct a triangle, given right angle, hypotenuse and side (RHS).

Key Vocabulary:

  • Angles: angles at a point, angles on a straight line, base angles, corresponding, alternate, interior, exterior, equidistant, prove, proof, supplementary, complementary;
  • Triangles: (equilateral, isosceles, right-angled, scalene);
  • Quadrilaterals: (quadrilateral, square, rectangle, rhombus, parallelogram, arrowhead, kite, edge, face, vertex, vertices congruent, tessellate);
  • Constructions: (construct, draw, measure, protractor, compasses, ruler, bisect(or), midpoint, congruent, tessellate, equidistant).

Suggested Lesson Outcomes:



Teaching & Learning Resources:

Measuring Resources
Angles Resources
Proof Resources
Constructions Resources
Loci Resources
Imperial Resources