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Right Angles

Age 11 to 14
Challenge Level Yellow starYellow star
Secondary curriculum
  • Problem
  • Getting Started
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Right Angles printable sheet
Link to a collection of printable sheets of circle templates.
 

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Can you work systematically to prove this?



Now try changing the number of points round the edge.
Can you do it now?

Can you show by calculation that the angle is a right angle?

What do you notice about the side of the triangle opposite the right angle?
 
Try this with other numbers of points round the edge.
When is it possible to make a right-angled triangle?
 
In this interactivity, the points are equally spaced around a circle. Imagine that they are not.
Can you explain the conditions which will give a right-angled triangle?
Can you prove this?


Many thanks to Geoff Faux who introduced us to the merits of the 9 pin circular geo-board.

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Not So Little X

Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?

The Cyclic Quadrilateral

This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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