Circle theorems lesson 8

A complete lesson on the theorem that a perpendicular bisector of a chord passes through the centre of a circle.

Assumes pupils can already use the theorems that:

1. The angle at the centre is twice the angle at the circumference
2. The angle in a semicircle is 90 degrees
3. Angles in the same same segment are equal
4. .Opposite angles in a cyclic quadrilateral sum to 180 degrees
5. A tangent is perpendicular to a radius
6. Angles in alternate segments are equal
7. Tangents from a point are equal
   so that more varied questions can be asked. Please see my other resources for lessons on these theorems.

Activities included:

Starter:
An animation reminding pupils about perpendicular bisectors, with the intention being that they would then practice this a few times with ruler and compass.

Main:

• Instructions for pupils to investigate the theorem, by drawing a circle, chord and then bisecting the chord.
• Slides to clarify the ‘two-directional’ nature of the theorem.
• Examples of missing angle or length problems using the theorem (plus another theorem, usually)
• A similar set of eight questions for pupils to consolidate.
• An extension prompt for pupils to use the theorem to locate the exact centre of a given circle.

Plenary:
An animation of the proof without words, the intention being that pupils try to describe the steps.

Printable worksheets and answers included.

Please review if you buy, as any feedback is appreciated!