| Euclides - 1871 - 136 pages
...two angles of a triangle be.equal, the sides wMch tubtend them are also equal. (Eucl. i. 6.) SE 2 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. -25 q _ Let the three sides of the A s ABO,... | |
| Bernard Marks - Geometry - 1871 - 172 pages
...side A B. 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... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...on equal spheres are mutually equilateral, they arc equivalent. Let ABC, DEF be two triangles which have the three sides of the one, equal to the three sides of the other, each to each, viz., AB to DE, AC to DF, and BC to EF ; then will the triangle ABC be equivalent to... | |
| Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...likewise those 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 - 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... | |
| 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... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...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... | |
| L J V. Gerard - 1874 - 428 pages
...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... | |
| Adrien Marie Legendre - Geometry - 1874 - 500 pages
...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... | |
| Benjamin Greenleaf - Geometry - 1874 - 206 pages
...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... | |
| |