Solving Geometrical Problems

Recognising and Demonstrating Key Geometric Properties

Grasping the core geometric properties related to triangles (equilateral, isosceles, right-angled) and quadrilaterals (rectangle, square, rhombus, parallelogram, trapezium).
Understanding the key properties of regular polygons with equal sides and angles.
Recognising congruent shapes which are identical in shape and size and similar shapes which have the same shape but different sizes.
Demonstrating proficiency in proving geometric relationships using properties of shapes.

Working With Geometric Transformations

Understanding the properties of reflections, translations, rotations, and enlargements in terms of fixed points, invariant points, lines and/or shapes.
Applying these properties to transform given shapes on a grid.
Recognising a transformation from its matrix.

Applying Theorems in Geometric Problems

Learning to apply Pythagoras’ theorem to calculate unknown lengths in right-angled triangles.
Utilising trigonometric relationships (sin, cos, tan) to tackle problems involving angles and sides in right-angled triangles.
Demonstrating ability to use the alternate segment, angles in a triangle, angles on a line, and interior and exterior angles theorems to find unknown angles in polygons and circles.

Dealing With Bearings and Distances

Interpreting and using bearings correctly, remembering that bearings are always measured clockwise from north and are usually given as three-digit numbers.
Employing scale factors to convert between real distances and distances on a map or scale drawing.

Completing Geometric Constructions

Demonstrating the ability to construct bisectors of lines and angles, perpendiculars, and triangles, given specific conditions.
Showing ability to use a pair of compasses, a ruler and a protractor to construct accurate drawings of shapes.

Solving Problems Involving Loci

Understanding the definition of a locus as the set of all points that satisfy certain conditions.
Drawing accurate loci based on given conditions, such as the locus of a point equidistant from two other points.
Determining regions bounded by loci to solve problems, for instance, in planning and design contexts.