Year 11 / Unit 2
Turn a diagram into a proof
A diagram suggests relationships; a proof names the conditions and the theorem that supports each step. Angles subtended by the same chord at the circumference agree when their vertices are on the same side of the chord.
The angle at the centre is twice the angle at the circumference standing on the same arc. Opposite angles in a cyclic quadrilateral sum to 180°, and a tangent is perpendicular to the radius at its contact point.
on the same arc
A cyclic quadrilateral has one angle of 112°. Find its opposite angle.
- Opposite angles of a cyclic quadrilateral sum to 180°.
- The angle is 180° − 112° = 68°.
Assumed knowledge
Use angle sums, parallel-line angle relationships, and triangle congruence and similarity. Recognise radii, chords and tangents, and justify geometric steps using stated conditions.
Study Specialist Mathematics alongside, or after, Mathematical Methods. Later units build on earlier units.
QCAA prior-learning guidance ↗