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
Special right triangle Ancient Egypt; that their surveyors did use ropes for measurement; that Plutarch recorded in "Isis and Osiris" (around 100 AD) that the Egyptians admired the 3 : 4 : 5 triangle; and that the Berlin Papyrus 6619 from the Middle Kingdom of Egypt (before 1700 BC) stated that "the area of a square of 100 is equal to that of two smaller squares. The side of one is ½ + ¼ the side of the other." The historian of mathematics Roger L. Cooke observes that "It is hard to imagine anyone being interested in such conditions without knowing the Pythagorean