G3c – The sum of angles in a triangle and the angle properties of polygons

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Part 1 – The sum of angles in a triangle

Teacher resources for Part 1

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  • Slides in PDF (one slide per page, suitable for importing into IWB software)
Links to past exam questions

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Interactive GeoGebra activity
Tick either box and drag the slider to see an animation of how the interior and exterior angles sum up to 180º and 360º respectively. You can reset the applet and move the white vertices of the triangle and try the animation again.
With thanks to Tim Brzezinski, whose Triangle Angle Theorems (V1) worksheet is available here. Material modified and embedded here under the CC-BY-SA 3.0 license.

Part 2 – Angle properties of polygons

Teacher resources for Part 2

Teachers: log in to access the following:

  • Slides in PDF (one slide per page, suitable for importing into IWB software)
Links to past exam and UKMT questions

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Interactive GeoGebra activity: Angle between regular polygons
In the real world

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Geodesic domes are very strong structures relative to the mass of materials involved in their construction. These domes are parts of a sphere structured around triangles or other shapes. The domes at the Eden Project are made up of outer layers of hexagons and pentagons, and inner layers of hexagons and triangles, for example.

Check out this article on geodesic domes from the Buckminster Fuller Institute for more – and note the equilateral triangles making up the dome in the article’s main image.