Students are taken through the discovery of various circle theorems. The theorems include, angle at the centre is twice the angle at the circumference, angles in the same segment and angles in cyclic quadrilaterals.Each circle theorem has an associated proof in the additional resources section. Once the theorems are discovered there is opportunity for students to consolidate their learning by calculating unknown angles.
Differentiated Learning Objectives
- All students should be able to discover the relationships between the angles at the centre and circumference of a circle, opposite angles in cyclic quadrilaterals and angles at the circumference in the same segment.
- Most students should be able to discover the three theorems and apply them individually to calculate missing angles.
- Some students should be able to discover and apply the three properties and apply them to calculate angles involving multiple theorems.