GSPThe Geometer’s Sketchpad

Dynamic geometry software can be used in a variety of ways in

• exploring and learning about the properties of shapes; • studying geometric relationships and learning geometrical facts;• transforming shapes;• working with dynamic images to make and test hypotheses aboutproperties of shapes;• making and exploring geometric constructions;• constructing and exploring loci.

Mathematics with ICT in Key Stage 3: Geometry lessons, 2004

2

Geometry with ICT

• 30 min to familiarise yourself (booklet for you to use in the session and take home)

Geometric Constructions

Subtended Angle Theorem 1• Imagine a circle

– Imagine a chord of that circle– Imagine the angle subtended

by the chord at the circumference

– Imagine the angle subtended by the chord at the centre

• How are these related?

Subtended Angle Theorem 2• Imagine a circle

– Imagine a chord– Imagine at one end of the

chord a tangent to the circle– Imagine also an angle

subtended by the chord at the circumference (away from the tangent)

• How are the angle between the tangent and the chord, and the angle subtended at the circumference, related?

• Handout with Activity 1, 2 and 3.