Oops, of course, if one side is 1 and other side is 2 the hypotenuse measures SQRT(5), not SQRT(3). But there is not a problem; you can construct a triangle with sides 1 and SQRT(2) at the 90 degrees angle, and the hypotenuse will measure SQRT(3). Francesc

Hello, you can draw this line, and you stated how: - Draw two perpendicular lines. - Take your compass and open it some width; it defines a unit. - With your compass measure, from the intersection of the two lines, measure one unit right and two units up. - Link the two resultant points with a line. This line measures SQRT(3). So you can effectively draw this line. Sum of angles of a triangle is 180 degree, yes, in an Euclidean geometry (plane geometry). But in other geometries this sum can be bigger, take this example: - Take the sphere as the surface of this geometry. - A "straight line" is the line that joins two points with the minimum length, in this case is a circle of maximum length. Over the sphere there are no paralel lines. - Consider the triangle defined by: the North Pole, the Ecuador at meridian 0, and the Ecuador at meridian 90. In this triangle all three angles measure 90 degrees. I cannot recommend you any bibliography, I'm not an expert on Geometry. But some articles about non-Euclidean Geometry in Wikipedia could be a good start in this theme. Regards, Francesc