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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?

Golden Triangle

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.

Darts and Kites

Explore the geometry of these dart and kite shapes!

Pentakite

Age 14 to 18
Challenge Level
Drw the diagram and work out all the angles. Can you seesimilar triangles? can you see congruent triangles?