 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...terminating in the other extremity of the base equal to one another. PROPOSITION VIII. If two triangles have the three sides of the one equal to the three sides of the other, each to each, then the triangles will also be equal to each other in every other respect, that is,... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...receive special attention. EQUALITY OP TBIANGLES. 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... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...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... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...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... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...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... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...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... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...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 pages
...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... | |
 | L J V. Gerard - 1874 - 428 pages
...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... | |
 | B. Marks - 1875 - 176 pages
...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... | |
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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. 
