Figure 4-13.-Constructing a right triangle with hypotenuseand one side given.EQUILATERAL TRIANGLE:LENGTH OF SIDE GIVENTo construct an equilateral triangle when thelength of a side is given, you can follow themethod previously described for constructing atriangle when the length of each side is given. Thesides of an equilateral triangle are equal in length.Each angle in an equilateral triangle measures60°. This fact is applied in the method ofconstructing an equilateral triangle with givenlength of side, such as the one shown infigure 4-14. Simply use a 30°/60° triangleand a T square or straightedge to erect lines fromA and B at 60° to AB.EQUILATERAL TRIANGLE IN AGIVEN CIRCUMSCRIBED CIRCLEA circumscribed plane figure is one thatencloses another figure, the circumscribed figurebeing tangent to the extremities of the enclosedfigure. An inscribed plane figure is one that isenclosed by a circumscribed figure.Figure 4-15 shows you how to inscribe anequilateral triangle within a given circumscribedcircle. Draw a vertical center line intersecting thegiven circle at A and B. With B as a center anda radius equal to the radius of the circle, strikearcs intersecting the circle at C and D. Linesconnecting A, C, and D form an equilateraltriangle.EQUILATERAL TRIANGLE ON AGIVEN INSCRIBED CIRCLEFigure 4-16 shows one method of circum-scribing an equilateral triangle on a given inscribedFigure 4-14.-Equilateral triangle with a given length ofside AB.Figure 4-15.-Equilateral triangle in a given circumscribedcircle.Figure 4-16.-Equilateral triangle on a given inscribedcircle: one method.4-5
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