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Exploring Geometric Properties with The Geometer's Sketchpad

The Geometer's Sketchpad (GSP) is dynamic geometry software essential for exploring and learning geometric properties. It enables students to study relationships, transform shapes, and make hypotheses about geometric facts through interactive images. In the context of Key Stage 3 mathematics, it aids in understanding concepts such as the Subtended Angle Theorem, which explores the relationship between angles and chords in circles. This resource includes a 30-minute familiarization session with a booklet for students to use, along with activities focused on geometric constructions and loci.

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Exploring Geometric Properties with The Geometer's Sketchpad

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  1. GSPThe Geometer’s Sketchpad

  2. Geometry with ICT 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 about properties of shapes; • making and exploring geometric constructions; • constructing and exploring loci. Mathematics with ICT in Key Stage 3: Geometry lessons, 2004

  3. 30 min to familiarise yourself (booklet for you to use in the session and take home)

  4. Geometric Constructions

  5. 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?

  6. 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?

  7. Handout with Activity 1, 2 and 3.

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