Triangle inequality ≥ b ≥ c" and "formula_8" is the golden ratio, as In the case of right triangles, the triangle inequality specializes to the statement that the hypotenuse is greater than either of the two sides, and less than their sum. The second part of this theorem is already established above for any side of any triangle. The first part is established using the lower figure. In the figure, consider the right triangle . An isosceles triangle is constructed with equal sides . From the triangle postulate, the angles in the right triangle satisfy: Likewise, in the isosceles triangle , the
Alan (given name) century, where it was about even with "Simon", and more numerous than "Henry". Early occurrences of the name in British records include: "Alanus" in 1066 (in the "Domesday Book"); and "Alain" in 1183. The name became popular in Scotland in part through the Stewarts. This family descends from Alan fitz Flaad, an Anglo-Breton knight, who possessed lands in what is modern day Shropshire, England. Alan (given name) Alan is a masculine given name in the English language. There are numerous differing etymologies attributed to the name. The name was first introduced into England by Bretons who took part in the