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

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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?