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Golden triangle in maths is any of the 10 congruent isosceles triangles formed by the adjacent vertices with the center of a regular polygon with 10 sides (decagon). Its angles are 36°, 72° and 72°. The length of the equal sides is equal to 1. The length of the base is φ = (√5 - 1)/2 = 2 / (√5 -1). 

When you draw the picture of a regular star (pentagram) with five pointed ends, the triangles at the end vertices are the golden triangles.

One property of this triangle is that if a bisector of base angles (72°) is drawn, it creates another golden triangle with the equal sides equal to the golden ratio φ.


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