MA27-07 Maths Coming soon
Circle theorem: alternate segment theorem
MA27-07
This lesson is coming soon.
In this lesson
Prove and use the alternate segment theorem, correctly naming it as the 'alternate segment theorem' and not confusing it with alternate angles on parallel lines.
What it covers
- The alternate segment theorem: the angle between a tangent and a chord equals the angle in the alternate segment
- Naming it correctly as 'alternate segment theorem', never 'alternate angle theorem'
- Not swapping in the supplementary angle by mistake
Key words
For: OCR GCSE J560, Edexcel IGCSE 4MA1, AQA GCSE 8300, Edexcel GCSE 1MA1, Eduqas GCSE C300, Cambridge IGCSE 0580
On the specification
| Board | Spec | Statement |
|---|---|---|
| OCR GCSE J560 | 8.05g | Apply and prove: for a point P on the circumference, the angle between the tangent and a chord through P equals the angle subtended by the chord in the opposite segment. |
| Edexcel IGCSE 4MA1 | H4.6C | Understand and use angle properties of the circle including: (i) angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the remaining part of the circumference (ii) angle subtended at the circumference by a diameter is a right angle (iii) angles in the same segment are equal (iv) the sum of the opposite angles of a cyclic quadrilateral is 180° (v) the alternate segment theorem |
| AQA GCSE 8300 | G10 | Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results |
| Edexcel GCSE 1MA1 | G10 | Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results |
| Eduqas GCSE C300 | HG10 | Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results |
| Cambridge IGCSE 0580 | E4.7 | Circle theorems I |
For teachers
This GCSE Maths lesson teaches circle theorem: alternate segment theorem. By the end, students should be able to prove and use the alternate segment theorem, correctly naming it as the 'alternate segment theorem' and not confusing it with alternate angles on parallel lines. It works through two worked examples and the mistakes examiners report.