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At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Darts and Kites

Explore the geometry of these dart and kite shapes!

No Right Angle Here

Prove that the internal angle bisectors of a triangle will never be perpendicular to each other.

Angles in Three Squares

Age 14 to 16
Challenge Level

The picture below shows three squares.
Surprisingly, $c = a + b$.
Can you prove it?

 

Once you've had a chance to think about how to prove it, click to reveal the diagram below.
Can you use the diagram to help you construct a proof?
 

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