An elementary treatise on geometry : simplified for beginners not versed in algebra . GEOMETRY. 98 QUERY ^, upon each of the three sides AB, AC^ BC, of anghtangled triangle ABC, you construct a square, whatrelation do the squares constructed upon the sides AC^BC, bear to the square constructed upon the hypothenusi^AB?. A. The square ABHK, constructed upon the hypothe-nuse AB, equals, in area, the two squares ACDE,BCGF, constructed upon the two sides AC, BC. Q. How can you prove it by this diagram, in whichthe perpendicular CM, is let fall from the vertex C, ofthe right-angled triangle ABC,
An elementary treatise on geometry : simplified for beginners not versed in algebra . GEOMETRY. 98 QUERY ^, upon each of the three sides AB, AC^ BC, of anghtangled triangle ABC, you construct a square, whatrelation do the squares constructed upon the sides AC^BC, bear to the square constructed upon the hypothenusi^AB?. A. The square ABHK, constructed upon the hypothe-nuse AB, equals, in area, the two squares ACDE,BCGF, constructed upon the two sides AC, BC. Q. How can you prove it by this diagram, in whichthe perpendicular CM, is let fall from the vertex C, ofthe right-angled triangle ABC, upon the hypothenuseAB, and extended until, in I, it meets the side HK,opposite to the hypothenuse; and DB and CH arejoined ? A. In the first place, I should remark that the twosides AB, AD, of the triangle ABD, are equal to the twosides AH, AC, of the triangle ACH, each to each (AH 94 GEOMETRY. and AB, being sides of the same square, ABHK; and,AC and AD, being sides of the square ACDE); andthat the angle DAB, included by the sides AD, AB, isalso equal to the angle CAH, included by the two sidesAC, AH (for each of these angles is formed by the angleCAB being added to the right angle of a s(iuare) ; there-fore these two triangles are equal to each other. (Query 1,Sect. II.) Q. Having proved that the triangle ABD is
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