The Elements of Geometry

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H. Holt, 1897 - Geometry - 227 pages
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Page 33 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...
Page 152 - 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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove = — • A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 13 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 197 - A sphere is a solid bounded by a surface, all the points of which are equally distant from a point within called the center.
Page 154 - Prove that, if from a point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and the part without the circle.
Page 84 - If four quantities are in proportion, they are in proportion by inversion; that is, the second term is to the first as the fourth is to the third. Let...
Page 14 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.
Page 147 - 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 94 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 185 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.

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