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By Francis J. Grund

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Additional 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

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A /\ Fig. II. Fig. UL GEOMETRY. ABC, If the two triangles, it is ed same manner, and after the side BC (Fig. ) the side AB that ; is ABC. three times as the side ab is, if is one third the side be one third of the side ABC, would The same figures, composed of any number of holds true of all similar, their sides are proportional to are different BC ; or not be similar to each other. There that the side ac must also be one third of the the triangles abc, proportion. half of the is also be half of the side BC If twice as is of the triangle abc, must be in propoT' if (Fig.

How can you prove it 1 A, Because the triangles, ABD, ABE, ABF, &c. are all right-angled in B ; and ABN, in every right-angled triangle, the greatest side is opposite to the right angle. ) Q. And what other truths do you derive from you have just mentioned ? A. 1st. The perpendicular AB measures the one the distance GEOMETRY. 45 MN ; for of the point A from the line can be drawn from that point it The angles 2dly. o, p, r, t, the shortest is to that line. line that ^c. , and, therefore, greater than the interior opposite right angle at B.

A triangle has one side and the two adjacent angles, equal to one side and the two adjacent angles in another triangle, each to each, the two triangles are equal. In equal triangles the equal angles are opposite 8. to the equal sides. 9 If two straight lines are perpendicular to a third line, they are parallel to 10. If two or so as to make the each other. lines are cut by a third intersection of a third line, equal to two line at equal angles, make the alternate angles equal, or so as to sum of the two interior angles formed by the two right angles, the lines are parallel.

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