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

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

Any triangle, for instance in the GEOMETRY. ABD, triangle one greater than another, AB 41 AB, is AD, the side side, which is and therefore, by -^ will contain a part AD ;* equal to AB taking upon the distance AD, and equal to joining (Q,uery 3, Sect. ) AC DC, the triangle ACD ; DBC, (Query 13, CBD, be still ADB, angle more still CBD than the angle so than the angle and the angle ; x, B, opposite to the smaller side in that ; AB, can be proved of two unequal sides ADB must consequently CBD opposite to the greater side at in the Sect.

N. D C -J jr^ They are parallel Q. How to each other. can you prove A. From the line CD this AB ; ? being parallel to AB, that every point in the line from the line F : CD and because is at EF is it follows an equal distance also parallel to AB, GEOMETRY. EF every point in the line from the line AB ; is an equal distance also at and therefore distances between the lines 33 CD Fig. ) and EF, or (in I^g. II] the differences between the equal distances, are equal that is, the lines CD, EF, are likewise equidistant ; and consequently parallel to each other.

CB, cb, loith respect to the ? are opposite to the equal angles at a QUERY IL If one side and the two adjacent angles in one triangle are equal to one side and tlie two adjacent angles in y. eacli„ lohat relation another triangle, each to do the two triangles bear to each other ? A. ) QUERY m. What remark can you make with respect angles at the basis of an isosceles triangk ? A. They are equal to each other. to the two GEOMETRY. Q. How can you prove it ? A. Suppose we had two equal isosceles triangles, ABC and abc, or, as ABC, were, another im- it of the triangle a5r, pression, that is, — AB, = AC, be = BC.

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