The Teaching of Geometry

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Ginn and Company, 1911 - Geometry - 339 pages
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Page 258 - Two triangles having 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 184 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Page 248 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 229 - Magnitudes are said to have a ratio to one another which are capable, when multiplied, of exceeding one another.
Page 190 - If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 144 - But when a straight line, standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a right angle, and the straight line which stands on the other is called a perpendicular to it (Def.
Page 127 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Page 295 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.
Page 299 - If two angles not in the same plane have their sides respectively parallel and lying on the same side of the straight line joining their vertices, they are equal, and their planes are parallel. Let the corresponding sides of angles A and A' in the planes MN and PQ be parallel, and lie on the same side of AA'.
Page 188 - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.

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