 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'...  Elements of Geometry: With, Practical Applications - Page 120by George Roberts Perkins - 1850 - 320 pagesFull view - About this book
 | Elias Loomis - Conic sections - 1849 - 252 pages
...similar. Wherefore, two triangles, &c. PROPOSITION XX. THEOREM. Two triangles are similar, when they have an angle of the one equal to an angle of the other, and the sides containing those angles proportional. Let the triangles ABC, DEF have the angle A of the one, equal... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...triangles include, by implication, those of all figures. 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. In the two triangles ABC, DEF, let the angles A... | |
 | 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 - 176 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 - 534 pages
...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 - 270 pages
...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... | |
 | Euclides - 1855 - 230 pages
...BC the segments of the base (c). PROPOSITION XIV. THEOREM [1.]—If equal parallelograms (AB and BC) have an angle of the one equal to an angle of the other, their sides about the equal angles are reciprocally proportional (DB is to BE, as GB is to BF). [3.]... | |
 | Peter Nicholson - Cabinetwork - 1856 - 518 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.... | |
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