Plane and Circle Geometry

Apply rule that if two lines are parallel to a third line then they are parallel to one another

Use angle relationships to identify parallel lines

Find angles at a point using angle relationships

Use angle relationships of parallel lines to find the size of unknown angles, giving reasons

Investigate and apply the exterior angle of a triangle property to find angles in a given diagram

Investigate and use the angle sum of a triangle property to find angles in a given diagram

Apply Exterior Angle Sum of Polygons

Apply the Interior Angle Sum of a Polygon formula

Apply the triangle inequality rule

Find unknown sides and angles in a given diagram by using the properties of special triangles and quadrilaterals

Apply the intercepts and parallel lines properties to find unknown sides

Application of congruent triangles to prove properties of special triangles and quadrilaterals

Write formal proofs of congruence of triangles, preserving matching order of vertices

Write formal proofs of similarity of triangles, preserving matching order of vertices

Scaling ratio for volume

Scaling ratio for area

Choosing a test for congruence (SSS test, SAS test, AAS test, RHS test)

Tests for similar triangles

Prove and apply tests for quadrilaterals using similarity results

Prove Pythagoras' theorem using similarity

Converse of Pythagoras' theorem

Equal chords subtend equal arcs on a circle, and conversely

A line through the centre of a circle perpendicular to a chord bisects the chord, and conversely

Chords equidistant from the centre of a circle are equal, and conversely

Equal arcs subtend equal angles at the centre of a circle, and conversely

Equal chords subtend equal angles at the centre and conversely

Angles at the circumference in the same segment are equal, and conversely

A radius (diameter) of a circle is perpendicular to the tangent at their point of contact

The angle between a tangent and a chord equals the angle at the circumference in the alternate segment

The angle at the centre is twice the angle at the circumference standing on the same arc

The angle at the circumference in a semi-circle is 90°, and conversely

Equal arcs subtend equal angles at the circumference, and conversely

Proving Quadrilaterals are Cyclic

The exterior angle of a cyclic quadrilateral equals the interior opposite (or remote) angle, and conversely

The opposite angles of a cyclic quadrilateral are supplementary, and conversely

Proving Concyclicity

Application of circle theorems

The products of the intercepts of two intersecting chords are equal, and conversely

The line joining the centers of two circles passes through their point of contact

The products of the intercepts of intersecting secants are equal

The Tangent-Secant Theorem

Tangents from an external point are equal.