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Prerequisites

G3a – Angles at a point, angles at a point on a straight line, vertically opposite angles
G3b – Alternate and corresponding angles on parallel lines
Knowledge of the definition of “regular” is also assumed

Part 1 – The sum of angles in a triangle

Teacher resources for Part 1

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Slides in PPTX (with click-to-reveal answers)
Slides in PDF (one slide per page, suitable for importing into IWB software)

Worksheet (with space for student work)
Handout (slides with exercises only; 4 per page for reduced printing)
- Worked solutions to questions

Skills drill worksheet – Isosceles triangles and angles (15 questions on one side of A4; answers included – requires knowledge of G4a)

Random Question Generator: Isosceles triangles and angles (requires knowledge of G4a)

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 PPTX (with click-to-reveal answers)
Slides in PDF (one slide per page, suitable for importing into IWB software)

Worksheet (with space for student work)
Handout (slides with exercises only; 4 per page for reduced printing)
- Worked solutions to all questions

Random Question Generator

Mashup activity: Exterior equations

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.

What next?