| George Washington Hull - Geometry - 1807 - 408 pages
...triangle, 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 1.... | |
| Dennis M'Curdy - Geometry - 1846 - 138 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 - 192 pages
...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, if... | |
| Euclid - Geometry - 1872 - 261 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 1 .... | |
| George Albert Wentworth - Geometry - 1877 - 442 pages
...A'B' B'C' =A'B', Hyp. Ax. 1 Cons. PROPOSITION VI. THEOREM. 284. Two triangles having an angle of the **one equal to an angle of the other, and the including sides proportional,** are similar. A A' In. the triangles ABC and A' B' С' let /А / Л1 * AB AC żA- żA', аж* _=_. We... | |
| George Anthony Hill - Physics - 1880 - 204 pages
...are 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 triangle... | |
| George Albert Wentworth - 1881 - 266 pages
...We'Hyp. Ax. 1 Since AE = A' B', Cons. PROPOSITION VI. THEOREM. 284. Two triangles having an angle of the **one equal to an angle of the other, and the including sides proportional,** are similar. A A' In the triangles ABC and A' B' C' let -. A'B' A'C' We are to prove А AB С and A'... | |
| Webster Wells - Geometry - 1886 - 392 pages
...tests of similarity (§ 268) is satisfied. PROPOSITION XX. THEOREM. 275. Two triangles are similar when **they have an angle of one equal to an angle of the other, and the** sides including these angles proportional. BC In the triangles ABC and A'B'C', let To prove that the... | |
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