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. Elements of Geometry - Page 9by Adrien Marie Legendre - 1825 - 224 pagesFull view - About this book
| Bernard Marks - Geometry - 1871 - 172 pages
...THEOREMS ILLUSTRATED. 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 part's. Let the two triangles ABC, ADC, have the side AB of the one equal... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...each to each, and the triangles themselves will be • •qua', Let ABC, DEF be two triangles having the three sides of the one equal to the three sides of the other, viz. : AB equal to DE. BC to EF, and AC to DF ; then' will the three angles also be equal, viz. : the... | |
| 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 BC =' EF ; then... | |
| 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, the angles of... | |
| 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 BC = EF ; then... | |
| 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 to DE, AC... | |
| 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 be equal to DE,... | |
| 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 AB equal to DE,... | |
| 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... | |
| 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... | |
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