 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...sum of DG and EG, by I. n ; and therefore EF is less than EG. I. 26. It will appear after I. 32 that two triangles which have two angles of the one equal to two angles of the other, each to each, have also their third angles equal. Hence we are able to include thu two cases of I.... | |
 | Euclides - 1883 - 176 pages
...Assuredly the proposition is not complete without a proof of this fact. EU. I. 26. THEOR. 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 (1st) the side adjacent to the equal angles... | |
 | Education - 1883 - 654 pages
...coincide with the vertex of the given angle and then the construction would fail. 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, viz., either the sides adjacent to the equal angles in... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...R. Therefore, the sum of the angles of a triangle equals two right angles. Cor.—If two triangles have two angles of the one equal to two angles of the other, the third angles will be equal. If, now, a = d and b = e, For, (1) a + b + c = 2 R. and (2) d + e +... | |
 | Mathematical association - 1883 - 86 pages
...[Alternative proofs, (i) by Theors. 16 and 5. (ii) By Theors. 7 and 5.] 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... | |
 | Woolwich roy. military acad - 1884 - 148 pages
...another. What 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,... | |
 | Euclides - 1884 - 94 pages
...Props. 1-26, Book I, are now published in a similar form to this. PROPOSITION XXVI. 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., either the sides adjacent to the equal angles in... | |
 | Mathematical association - 1884 - 146 pages
...that the 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... | |
 | Palaestra Oxoniensis - 1884 - 204 pages
...three given straight lines, of which any two are together greater than the third. (5) If two triangles have two angles of the one equal to two angles of the other, each to each, and have one side equal to one side, viz. either the sides adjacent to the equal angles... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...angles A and B by AF and BF, and the angles a and 6 by af 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= AB2 : o&2 (Theo. XIV). Multiplying first couplet... | |
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If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent. 
