 | 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.... | |
 | Dennis M'Curdy - Geometry - 1846 - 166 pages
...have their sides about the equal angles reciprocally proportional : and triangles are equal, which have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional. Given two equal triangles ABC, ADE,... | |
 | 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,... | |
 | 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.... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...ABC ABD The same is true of parallelograms. BE BF' VI. Theorem. If two triangles have an angle of the one equal to an angle of the other, the ratio of their areas is equal to that of the products of the sides which contain those angles. ELEMENTS OF GEOMETRY. [BOOK... | |
 | 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... | |
 | 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... | |
 | Euclid - Geometry - 1890 - 442 pages
...parallelograms have t-uuo adjacent sides of the one respectively equal to two adjacent sides of the other, and an angle of one equal to an angle of the other, the parallelograms are identically equal. Let £ZJ' ABCD, PQRS, have AB = PQ, AD = PS, i AA pg and A =... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...triangle are given, the remaining side may be found from one of the three equations just written. Ex. 161. If two triangles have an angle of one equal to an...equals the ratio of the products of the sides including the equal angles. AABCAB x AC . ____ \A B' C AB'xAC •. SUG. Connect B and C'. Compare each A with... | |
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... 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. 
