 ... 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.  Plane Geometry - Page 148by Claude Irwin Palmer, Daniel Pomeroy Taylor - 1915 - 277 pagesFull view - About this book
 | Euclides - 1846 - 272 pages
...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 - 168 pages
...sides and angles of a parallelogram are equal: p. 34 ofb. 1. (d)p. 11, 5; (c)p. 9,5. 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, having... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...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 - 284 pages
...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 - 436 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 ¿A- ¿A',... | |
 | 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 triangle... | |
 | George Albert Wentworth - Geometry, Modern - 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... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...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... | |
 | Webster Wells - Algebra - 1890 - 560 pages
...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. Therefore... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...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 sides including the equal angles proportional, the triangles are similar. PROPOSITION XVIII. The ratio... | |
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