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Circle Theorems

Explore five circle theorems by moving lines and points around the TI-Nspire screen.

Barrie Galpin

Fach:

Schlagwörter Temperature

Students are able to explore the following circle theorems:

· the angle at the centre is twice the angle at the circumference;

· angles from the same arc in the same segment are equal;

· the angle in a semicircle is a right angle;

· opposite angles in a cyclic quadrilateral add up to 180°;

· the tangent to a circle at a point is perpendicular to the radius

In each case students are encouraged to discover the theorem for themselves before seeing a formal statement . However the activities do not prove the circle theorems.  Instead they give students the opportunity to get a sense of how the theorems work, as they move points and lines around and see what happens.

There is .ts file with 14 pages, supported by detailed instructions on a 3-page student handout and teacher notes. The activity forms part of the OxBox, published by Oxford University Press  to support their course 'Oxford GCSE Maths'.  http://www.oup.com/oxed/secondary/2010gcse/