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Pentakite
Age 14 to 18
Challenge Level 
Draw out a copy of the diagram, and it will help if you draw on the triangle DAC.
Mark on any angles that you can calculate.
There are various ways you can show that two triangles are congruent, which are sometimes called RHS, SSS, SAS, ASA. Since you know more angles than sides, the ASA condition is probably most helpful.
Two triangles are similar if they have the same set of angles. Similar triangles are enlargements of each other.
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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?
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.
