Texas Mathematics Teachers' Bulletin . (1) A right angle. From the vertex A of the right angle DAB measure on one ofits sides a segment AB and on this segment describe an equilat-eral triangle ABC, then the angle CAD is one-third of the rightangle 0_ B. F:^.^. (2) An angle of 108° can readily be constructed and tri-sected. The tenth proposition of the Fourth Book of Euclid,viz.: Construct an isosceles triangle having each of the baseangles double the remaining angle does this. In fact, theproblem occurs in our common school texts on geometry in theinscription of a regular decagon in a ci
Texas Mathematics Teachers' Bulletin . (1) A right angle. From the vertex A of the right angle DAB measure on one ofits sides a segment AB and on this segment describe an equilat-eral triangle ABC, then the angle CAD is one-third of the rightangle 0_ B. F:^.^. (2) An angle of 108° can readily be constructed and tri-sected. The tenth proposition of the Fourth Book of Euclid,viz.: Construct an isosceles triangle having each of the baseangles double the remaining angle does this. In fact, theproblem occurs in our common school texts on geometry in theinscription of a regular decagon in a circle. Assuming therefore that ABC (Fig. 2) is an isosceles trianglesuch that angle ABC equals angle BCA equals twice angle BAC 8 University of Texas Bulletin produce CB, then angle ABD equals angles BCA and BAG andsince angle BCA is twice angle BAG hence ABD equals threetimes angle BAG. Since BAG is 36°, and ABG 72° angle ABDis 108°. If an equilateral triangle BEG is described on BC theangle EGA=angle AGB—angle EGB=72°—60°=12°. Gonse-quently an angle of 36° can be trisected. If an equilaterial triangle FAG is described on AC then angleFAB=angle FAG—angle BAC=60°—36°=24°. Hence angle FAB equals one-third, of angle ABC; that is
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