Plane Geometry

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Macmillan, 1923 - Geometry, Modern - 232 pages
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Page 182 - The area of a rectangle is equal to the product of its base and altitude ; that is, A = ab. 443. Corollary 1. The area of a square is equal to the square of its side. 444. Corollary 2. Tiro rectangles are to each other as the products of their bases and altitudes.
Page 58 - If two parallel lines are cut by a transversal, the alternate interior angles are equal.
Page 99 - Any two sides of a triangle are together greater than the third side.
Page 73 - If two triangles have two sides of the one equal to two sides of the...
Page 271 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. OM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'.
Page 329 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180 and less than 540. (gr). If A'B'C' is the polar triangle of ABC...
Page 74 - XVIII, prove that the perpendicular is the shortest line that can be drawn from a point to a straight line.
Page 103 - The Radius of a sphere is a straight line drawn from the center to any point in the surface.
Page 164 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 30 - Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other.

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