 If two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. Given two triangles ABC and A'B'C', having the angle A equal to the angle A'.  The Elements of Plane Geometry - Page 180by Charles Austin Hobbs - 1899 - 240 pagesFull view - About this book
 | George Washington Hull - Geometry - 1807 - 408 pages
...they are similar to each other. PROPOSITION XVIII. THEOREM. 254. Two triangles are similar when they have an angle of one equal to an angle of the other, ancL the sides including these angles proportional. *BD* Given — The triangles ABC and DEF, with... | |
 | Rev. John Allen - Astronomy - 1822 - 516 pages
...HG, and of PB to BL or HE. Cor. 1. — By a similar reasoning it may be proved, that triangles, which have an angle of one, equal to an angle of the other, are to each other, in a ratio, compounded of the ratios, of the sides including the equal angles. Cor.... | |
 | Euclides - 1846 - 272 pages
...equal angles are reciprocally proportional (AB to BC as 1.I! to BD. And if two triangles (ABD and CBL), have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, they will be equal to one another. PART... | |
 | Dennis M'Curdy - Geometry - 1846 - 166 pages
...opposite sides and angles of a parallelogram are equal : p. 34ofb. 1. 15 Th. Equal triangles which have an angle of one equal to an angle of the other, have their sides about the equal angles reciprocally proportional : and triangles are equal, which... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...that ab : AB :: be : BC ; and by making C the centre, that be : BC :: ac : AC. COR. 1. Conversely, if two triangles have an angle of one equal to an angle of the other, and the sides forming the equal angles proportionals, the triangles will be similar. COR. 2. Hence, also,... | |
 | Euclid - Geometry - 1872 - 284 pages
...equal angles are reciprocally proportional (AB to BC as LB to BD). And if two triangles (ABD and CBL), have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, they will be equal to one another. PART... | |
 | George Anthony Hill - Physics - 1880 - 204 pages
...equiangular with respect to each other. (b) K they have their homologous sides proportional. (c) If they have an angle of one equal to an angle of the other, and the sides including these angles proportional. (18) The perpendicular upon the hypothenuse of a right... | |
 | Webster Wells - Algebra - 1890 - 560 pages
...similar, as also are the triangles EOG and COD ; for, by Geometry, two triangles are similar when they have an angle of one equal to an angle of the other, and the including sides proportional. Then the figure OFEG is similar to OBDC, and hence OFEG is a parallelogram.... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...the base, PROPOSITION XV. Two triangles which are mutually equiangular are similar. PROPOSITION XVI. If two triangles have an angle of one equal to an angle of the other, and the side* including the equal angles proportional, the triangles are similar. PROPOSITION XVII. Two... | |
 | Electronic journals - 1922 - 560 pages
...and there is no limit to the number of independent solutions. We can also state now this theorem: // two triangles have an angle of one equal to an angle of the other, and if in each triangle the n-th power of the side opposite is equal to the sum of the n-th powers of the... | |
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