GCSE Mathematics — Geometry

Led by Euclid Simulacrum

The sixth module of the OCR GCSE Mathematics course — constructions, angle facts, properties of polygons and circle theorems. Hosted by Euclid Simulacrum.

1. Module 1

   Conventions, Constructions and Loci

   Led by Euclid Simulacrum

   The question

   Geometric vocabulary and notation, the four ruler-and-compass constructions (perpendicular bisector, angle bisector, perpendicular from/at a point), and applying constructions to loci problems. Full 2D and 3D shape terminology.

   Outcome

   The student can perform constructions accurately and solve loci problems using them. (Construction geometry)

   Sub-units

   1. ○ 1.1 Conventions, Constructions and Loci Open this unit → ✓ ↻
   Begin the course → Print certificate of completion
2. Module 2

   Angles and Properties of Polygons

   Led by Euclid Simulacrum

   The question

   Angle facts (at a point, on a line, vertically opposite, alternate, corresponding), the angle sum of triangles and polygons, the interior angle of regular polygons, properties of triangles and all six quadrilateral types, and simple geometrical proofs using stated reasons.

   Outcome

   The student can apply angle facts and shape properties to find unknowns and construct simple proofs. (Angle and shape reasoning)

   Sub-units

   1. ○ 2.2 Angles and Properties of Polygons Open this unit → ✓ ↻
   Open this module → Print certificate of completion
3. Module 3

   Circle Theorems

   Led by Euclid Simulacrum

   The question

   The six major circle theorems — angle at centre, angle in semicircle, angles in same segment, cyclic quadrilateral, tangent-radius, alternate segment — applied to find unknown angles and proved from first principles at Higher tier.

   Outcome

   The student can state, apply and prove the circle theorems. (Circle geometry)

   Sub-units

   1. ○ 3.3 Circle Theorems Open this unit → ✓ ↻
   Open this module → Print certificate of completion