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

By Francis J. Grund

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Will you now 2. 1. first EFC, the two re- case, viz : two straight which two ? a third line at equal angles. they are cut by a third line so as to alternate angles equal 3. also equal must be equal (Truth state the different cases in Tllien they are cut by When is at equal angles. straight lines are parallel A. angle CFN and you have again the ; lines cut CFN and and therefore, by taking from each of the equal sums the maining angles For the sum each other. EFC ; make the and, Wlien the sum of the two interior angles, made by of a third line, is equal to two right the intersection angles.

Q. 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.

In a right-angled triangle, the right angle to the ^ sum of the two The teacher may now of these principles. * ask his pupils to repeat the demonstn- SECTION II. OF EQUALITY AND SIMILARITY OF TRIANGLES. PART I. OF THE EQUALITY OF TRIANGLES. Preliminary Remark. There considered in triangles, viz the shape larity ; are three kinds of equality to be equality of area, without reference to : equality of shape, without reference to the area ; and equality of both shape and area coincidence.

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