Pythagorean theorem straightedge and compass. Pythagoras's theorem enables construction of incommensurable lengths because the hypotenuse of a triangle is related to the sides by the square root operation. The figure on the right shows how to construct line segments whose lengths are in the ratio of the square root of any positive integer. Each triangle has a side (labeled "1") that is the chosen unit for measurement. In each right triangle, Pythagoras's theorem establishes the length of the hypotenuse in terms of this unit. If a hypotenuse is related to the unit by the square root of a positive integer that is
Right angle be made quickly and without technical instruments. The geometric law behind the measurement is the Pythagorean theorem ("The square of the hypotenuse of a right triangle is equal to the sum of the squares of the two adjacent sides"). Thales' theorem states that an angle inscribed in a semicircle (with a vertex on the semicircle and its defining rays going through the endpoints of the semicircle) is a right angle. Two application examples in which the right angle and the Thales' theorem are included (see animations). Right angle In geometry and trigonometry, a right angle is an angle of exactly