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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... An Elementary Treatise on Plane and Solid Geometry - Page 146by Benjamin Peirce - 1871 - 150 pagesFull view - About this book
| George Roberts Perkins - Geometry - 1850 - 332 pages
...also be proportional to the sides GH, HK, (B. IV, Def. III.) Therefore, the two triangles ABC, GHK **have an angle of the one equal to an angle of the other, and the sides** about those angles proportional, and consequently these triangles are similar; and being similar, we... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...include, by implication, those of all figures. B 109 D DF., PROPOSITION XX. THEOEEM. 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. Let ABC, DEF, be two triangles, having the angle... | |
| Euclid - Geometry - 1853 - 136 pages
...(a) Hypoth. (41 I.29. (c) I. 26. fa) I. 29. (6) Hypoth. (c) I. 34. COROLLARY 2. If two parallelograms **have an angle of the one equal to an angle of the other,** the remaining angles shall be respectively equal. For the angles opposite the equal angles are equal... | |
| Charles Davies - Geometry - 1854 - 436 pages
...by implication, those of all f1gures. BOOK IY. 109 D PROPOSITION XX. THEOREM. 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. Let ABC, DEF, be two triangles, having the angle... | |
| William Somerville Orr - Science - 1854
...the other, have their sides about the equal angles reciprocally proportional ; and triangles which **have an angle of the one equal to an angle of the other, and** their sides about those angles reciprocally proportional, are equal to one another. Let the triangles... | |
| Euclides - 1855
...equal to an angle of the other. If triangles are equiangular . If triangles are similar . . If equal **triangles have an angle of the one equal to an angle of the other.** If triangles have an angle in the one equal to an angle in the other, and their sides about the equal... | |
| Euclides - 1855
...compounded of the ratios which are the game with the ratios of the sides. Corollary 1. — Triangles which **have an angle of the one equal to an angle of the other,** are to one another as the rectangles contained by the sides about those angles. Corollary 2. — Equiangular... | |
| Peter Nicholson - Cabinetwork - 1856 - 482 pages
...equal to the sum of the two lines AD, DB, therefore AB'=AC*+BC9. THEOREM 54,. 125. Two triangles, which **have an angle of the one equal to an angle of the other,** are to each other as the rectangle of the sides about the equal angles. Suppose the two triangles joined,... | |
| George Roberts Perkins - Geometry - 1856 - 460 pages
...other, and the sides containing the equal angles proportional. Two rhombuses are similar, when they **have an angle of the one equal to an angle of the other.** All squares are similar figures. All regular polygons of the same number of sides are similar figures.... | |
| Euclides - 1859
...àvriirtirèvQaaiv at ir\tvpai, ai irepi ràç; îffaç ywviaç, laa iariv iKtlva. Equal triangles which **have an angle of the one equal to an angle of the other** have their sides about the equal angle* reciprocally proportional ; and triangles which have an angle... | |
| |