Seven activities in which students investigate angles in circles using basic geometric constructions.
Students start with a new, blank TI-Nspire document and, using a worksheet for guidance, work through the necessary constructions. The seven investigations are:
· Triangle on a Chord and Centre
· Perpendicular Bisector of Chords
· Inscribed Angle Theorem
· Angle in a Semicircle
· Tangent to a Circle
· The Tangent Kite
· The Cyclic Quadrilateral
In each case students are able to move points and see how the measurements of angles change. This will convince them that a particular result always seems to be true. They are then encouraged to prove the result, either using an algebraical or a geometrical approach.