Circle theorems lesson 5

A complete lesson on the theorem that a tangent is perpendicular to a radius.

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
   so that more varied questions can be asked. Please see my other resources for lessons on these theorems.

Activities included:

Starter:
Some basic recap questions on theorems 1 to 4

Main:

• Instructions for pupils to discover the rule, by drawing tangents and measuring the angle to the centre.
• A set of six examples, mostly using more than one theorem.
• A set of eight similar questions for pupils to consolidate.
• A prompt for pupils to create their own questions, as an extension.

Plenary:
A proof by contradiction of the theorem.

Printable worksheets and answers included.

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