 | Edward Olney - 1872 - 472 ページ
...attention. A BD rV H E EQUALITY OF TRIANGLES. PROPOSITION IX. 292. Theorem. — Two triangles which have the three sides of the one equal to the three sides of the other, each to each, are equal. DEM. — Let ABC and DEF be two triangles, in which AB = DE, AC = DF, and BC = EF ; then... | |
 | Benjamin Greenleaf - 1873 - 202 ページ
...shown that is not equal to it ; hence the angle A must be greater than the angle D. THEOREM XHI. 58. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles themselves will be equal. Let the triangles ABC, DEF have the side AB equal to DE, AC... | |
 | Benjamin Greenleaf - 1874 - 206 ページ
...shown that is not equal to it ; hence the angle A must be greater than the angle D. THEOREM XIII. 58. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles themselves will be equal. • Let the triangles ABC, DEF have the side AB equal to DE,... | |
 | Adrien Marie Legendre - 1874 - 500 ページ
...would be contrary to the hypothesis : hence, EAG must be greater than EDF. PROPOSITION X. THEOREM. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles will be equal in all their parts. In the triangles ABC and 'DEF, let AB be equal to DE,... | |
 | L J V. Gerard - 1874 - 428 ページ
...perpendicular sides of the other, each to each, they are equal to each other. THEOREM 18. (Eucl. I. 8.) If two triangles have the three sides of the one equal to the three sides of the other, eaeh to each, they are equal to each other. Let ABC and DEF be two triangles having the sides AB, BC... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 ページ
...to the side DC, aud the side AD to the side BC. Join AC. Comparing the two triangles ABC and ADC, we have the three sides of the one equal to the three sides of the other (hyp. and const.). Therefore the alternate angles BAC and DCA are equal, (I. 6). and therefore AB is... | |
 | Euclides - 1874 - 120 ページ
...so that the angles ARO and AOR are equal. Bisect RO in I) and join AD. Then the triangles ARD, AOD have the three sides of the one equal to the three sides of the other, and therefore by I. 8 we can prove the angles at A equal to one another and likewise the angles at... | |
 | B. Marks - 1875 - 176 ページ
...angle c, opposite the side A B. DB PROPOSITION XIX. THEOREM. DEMONSTRATION. We wish to prove that, If two triangles have the three sides of the one equal to the three sides of the other, each to each, they are equal in all their parts. Let the two triangles ABC, ADC, have the side AB of the one equal... | |
 | Association for the improvement of geometrical teaching - 1876 - 66 ページ
...unequal,; the base of that which has the greater angle being greater than the base of the other. THEOR. 15. If two triangles have the three sides of the one equal...triangles are identically equal, and of the angles [Alternative proofs, (i) by Theors. 14 and 5. (ii) By Theors. 6 and 5.] THEOR. 16. If two triangles... | |
 | Euclides, James Hamblin Smith - 1876 - 376 ページ
...triangle be equal, the sides which subtend them are also equal. (Eucl. I. 6.) SB * PROPOSITION 0. THEOREM. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles must be equal in all respects. JS~ OS Let the three sides of the A s ABC, DEF be equal,... | |
| |
If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent. 
