First. An equilateral triangle, [Fig. 118]. On the ends of a given base A B, with A B as a radius describe arcs cutting at C, and draw A C, C B.
Second. Triangle of unequal sides, [Fig. 119]. On either end of the base A D, with the side B as a radius describe an arc; and with the side C as a radius, on the other end of the base as a center, describe arcs cutting the arc at E; join A E, D E.
This construction may be used for finding the position of a point C or E at given distances from the ends of a base, not necessarily to form a triangle.
Fig. 120.
Fig. 121.
Ex. 16.—To construct a square rectangle on a given straight line.
First. A square, [Fig. 120]. On the ends B A as centers, with the line A B as radius, describe arcs cutting at C; on C describe arcs cutting the others at D E; and on D and E cut these at F G. Draw A F, B G and join the intersections H I.
Second. A rectangle, [Fig. 121]. On the base E F draw the perpendiculars E H, F G, equal to the height of the rectangle, and join G H.