Geometry

Angles are classified by their measure in degrees — acute, right, obtuse, straight, and reflex. Understanding angle types is the foundation of geometry.

Angles on a straight line sum to 180°. Angles around a full point sum to 360°. Vertically opposite angles are always equal.

When a transversal crosses two parallel lines, it creates pairs of equal angles (corresponding and alternate angles) and supplementary angle pairs (co-interior angles that add up to 180°).

The sum of the interior angles of any polygon depends only on the number of sides. For an n-sided polygon the sum is (n − 2) × 180°. Regular polygons have all angles equal, so each interior angle = sum ÷ n.

The angle sum property of triangles and exterior angle theorem with examples.

A compound shape is made up of two or more simple shapes joined together. To find the total area, split the compound shape into rectangles, triangles, or other familiar shapes, calculate each area separately, and add them up.

Explore the units used to measure length, mass, time, and volume, and practise converting between them using the correct conversion factors.

Formulas for the area and perimeter of a parallelogram with worked examples.

Formulas for the area and perimeter of a rectangle, including worked examples.

Formula cards for the area and perimeter of all common 2D shapes.

Formulas for the area, perimeter, and diagonal of a square, with worked examples.

Formulas for the area and perimeter of a trapezoid with worked examples.

How to calculate the area and perimeter of triangles using base-height and Heron's formula.

An arc is part of the circumference; a sector is a pie-slice of a circle. Both are calculated as a fraction of the full circle, where the fraction = angle ÷ 360.

Formulas for the area and circumference of a circle, and how to apply them.

The circumference is the distance around the outside of a circle. It equals π multiplied by the diameter, or 2π multiplied by the radius.

An angle is formed by two rays sharing a vertex. Learn to identify angle types, use a protractor to measure angles, and draw angles of any given size.

A triangle is a three-sided polygon. Learn the triangle inequality, how to construct triangles from given measurements using compass and ruler, and the main types of triangles.

A line segment is a straight path between two fixed points. Learn how to draw segments of a given length, measure them, and find the midpoint using a compass.

The coordinate plane uses two perpendicular number lines (axes) to locate any point using an ordered pair (x, y). It is divided into four quadrants.

The gradient (slope) of a line measures how steep it is — how much the line rises or falls for every unit it moves to the right. Gradient = change in y ÷ change in x (rise ÷ run).

The midpoint of a line segment is the point exactly halfway between its endpoints. The distance formula uses Pythagoras' theorem to find the straight-line distance between any two points on a coordinate grid.

Every straight-line graph can be written as y = mx + c, where m is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis). Knowing these two values is enough to draw or describe any straight line.

Study of shapes, space, and measurement covering angles, areas, volumes, coordinates, and spatial reasoning.

Formulas for the volume and surface area of a cone with worked examples.

How to calculate the surface area and volume of a cube and rectangular box.

Formulas for the volume and surface area of a cuboid (rectangular box) with worked examples.

Formulas for computing the surface area and volume of a cylinder.

Formula cards for the volume and surface area of all common 3D solids.

Formulas for the volume and surface area of a sphere with worked examples.

A shape has line symmetry when it can be folded along a line so that both halves match exactly. Learn to identify axes of symmetry in common shapes, regular polygons, and everyday letters.

A shape has rotational symmetry when it looks the same after being rotated less than a full turn about a fixed centre point. Explore the order of rotational symmetry and point (central) symmetry.