An elementary treatise on geometry : simplified for by Francis J. Grund

By Francis J. Grund

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Extra resources for An elementary treatise on geometry : simplified for beginners not versed in algebra. Part I, containing plane geometry, with its application to the solution of problems

Example text

Successively greater, as the are more remote from the and, therefore, the sides which are successively opposite triangles AD For the angles ; ADE, AEF, &c. Sfc. , to these angles, in the ADE, AEF, AFN, must become greater with them. othly. sides of, AB, are equal. the side BD The straight lines, AC, AD, drawn on both and at an equal distance from, the perpendicular AB For the two triangles common, and the side BC ABC, ABD, have equal to the side AC, AD, are at an equal distance AB) and as the line AB is perpendicular to CD, the angle ABC, included by the sides AB, BC, in the triangle ABC, is equal to the angle ABD, (because the lines from the perpendicular ; GEOIETRY.

C D DM C MB A The angle AJSIB, made hy the lines A. always greater than the angle AB, lines ABC; in the triangle AM, MB, two sides Q. A. The AM, BM, is opposite to the side hut the sum of the two sum of the in all cases smaller than the AC, CB, of How the triangle. can you prove both your assertions ? exterior angle angle rior opposite 13, Sect. ) angle is ACB, AMB ; and MDB ACD, for greater is in the greater than the intetriangle the same reason is ACD (Query the exterior than the interior opposite angle GEOMETRY.

QUERY XL If you have two to two sides, AB, BC, of ABC, another triangle, each to ABC included by the two sides, AB, each; hut the angle BC, of a triangle, abc, equal sides, ab, be, in the triangle A BC, greater than the angle abc, included by the sides ab, be, in the triangle abe remark can you make with regard AC, which are respectively opposite to those angles A. Thcct the side ac, opposite in the triangle abc, to the greater angle Q. A. ABC, How By is do you prove placing the in the triangle this will fall loithin the angle AB ABC, ABC ; upon the line AC opposite upon the triangle abc (its equal), the side be because the angle abc and the extremity see* in the figure beforf you, or within Is*.

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