An elementary treatise on geometry : simplified for beginners not versed in algebra . gles are equal toecLch other. For, in this case, we have two sides, andthe right angle which is opposite to the greater of th^m,in the one, equal to two sides, aad the angle which isopposite to the greater of them, in the other. 48 GEOMETRY. Q. But if, in Fig. II. (page 46) the two sides AC, AB, and theangle at C, opposite to the smaller side AB, be given, would notthis be sufficient to determine the triangle ABC ? A. No. For the two lines, AB, AE, being equal, there wouldbe two triangles, ABC and AEC possibl
An elementary treatise on geometry : simplified for beginners not versed in algebra . gles are equal toecLch other. For, in this case, we have two sides, andthe right angle which is opposite to the greater of th^m,in the one, equal to two sides, aad the angle which isopposite to the greater of them, in the other. 48 GEOMETRY. Q. But if, in Fig. II. (page 46) the two sides AC, AB, and theangle at C, opposite to the smaller side AB, be given, would notthis be sufficient to determine the triangle ABC ? A. No. For the two lines, AB, AE, being equal, there wouldbe two triangles, ABC and AEC possible, containing the samethree things, and it would be doubtful which of the two triangleswas meant. QUERY XL If you have two sides, ab, be, of a triangle, abc, equalto two sides, AB, BC, of another triangle, ABC, each toeach; hut the angle ABC included by the two sides, AB,BC, in the triangle A BC, greater than the angle abc,included by the sides ab, be, in the triangle abe; whatremark can you make with regard to the two sides ac,AC, which are respectively opposite to those angles ?. A. Thcct the side ac, opposite to the smaller angle abc,in the triangle abc, is smaller than the side AC, oppositeto the greater angle ABC, in the triangle ABC. Q. How do you prove this ? A. By placing the triangle abc upon the triangleABC, with the side ab upon AB (its equal), the side bewill fall loithin the angle ABC, because the angle abc issmaller than the angle ABC; and the extremity c, of theline be, will either fall without the triangle ABC, as yousee*in the figure beforf you, or within it, or it may alsofell upon the line AC itself. Is*. If it falls without the triangle ABC, by imagining GEOxMETRY. 49 the line Cc drawn, the triangle cBC will be isosceles; forwe have supposed the side be equal to BC; and becausethe angles at the basis of an isosceles triangle are equal(Query 3, Sect. II.), the angle z is equal to the sum ofthe two angles z and y ; consequently greater than theangle y alone; a
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