An Examination Manual in Plane Geometry

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Ginn, 1896 - Geometry - 138 pages
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Page 106 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 127 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 110 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...
Page 129 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 126 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the Jingle.
Page 92 - Find the angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle.
Page 123 - The product of two sides of a triangle is equal to the product of the altitude on the third side and the diameter of the circumscribed circle.
Page 118 - DE'F, and consequently symmetrical with DEF. PROPOSITION XIII.—THEOREM. 55. Two triangles on the same sphere are either equal or symmetrical, when a side and two adjacent angles of one are equal respectively to a side and two adjacent angles of the other.
Page 129 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Page 122 - If the radius of a circle be divided in extreme and mean ratio, the greater segment is equal to one side of a regular inscribed decagon.

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