 | Euclides - 1884 - 214 pages
...it would be a proof of both the sixteenth and seventeenth. It shows us that, if two triangles have two angles of the one equal to two angles of the other, each to each or together, their third angles are also equal. The corollaries to this proposition are... | |
 | Mathematical association - 1884 - 146 pages
...straight line joining their vertices bisects the vertical angles. THEOR. 19. If two triangles have two angles of the one equal to two angles of the other, each to each, and have likewise the sides opposite to one pair of equal angles equal, then the triangles... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...A and B by AF and BF, and the angles a and b by of and bf. Now, since the triangles ABF, abf, have two angles of the one equal to two angles of the other, they are similar (Cor., Theo. IX) ; hence, ABF : abf = AB 2 : a& 2 (Theo. XIV). Multiplying first couplet... | |
 | Euclides - 1884 - 182 pages
...equality of triangles ; the first of which may be separately enunciated thus : If two triangles have two angles of the one equal to two angles of the other, each to each, and also the sides adjacent to these angles equal ; they shall have all their other elements... | |
 | Oxford univ, local exams - 1885 - 358 pages
...four sided figures, and the four definitions concerning segments of circles. 2. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side; viz. the sides adjacent to the equal angles in each;... | |
 | Lewis Carroll - Geometry - 1885 - 318 pages
...respects.' This contains a superfluous datum : it would have been enough to say ' if two Triangles have two angles of the one equal to two angles of the other &c.' Nie. Well, it is at worst a superfluity : the enunciation is really identical with Euclid's. Min.... | |
 | United States. Congress. Senate - United States - 1880 - 1304 pages
...on the other side of the given what figure will the two triangles forra f 2. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, namely, either the sides adjacent to the equal angles,... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...from two right angles, the remainder is equal to the third angle. 140. COR. 2. If two triangles have two angles of the one equal to two angles of the other, the third angles are equal. 142. COE. 4. In a triangle there can be but one right angle, or one obtuse... | |
 | E. J. Brooksmith - Mathematics - 1889 - 356 pages
...other converse proposition may be obtained from Proposition V., Book I. ? 3. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, namely, the sides opposite to the equal angles in each,... | |
 | William Ernest Johnson - Plane trigonometry - 1889 - 574 pages
...draw IX, IT, IZ perpendiculars on the sides. Then, the triangles BXI, BZ1 having a common side BI and two angles of the one equal to two angles of the other, are equal in all respects, so that IX=IZ. Similarly IX=IY, :.IY=IZ. Therefore, the triangles AZI, A... | |
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If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. 
