| Euclides - 1871 - 136 pages
...If 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...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, DEF be equal, each to each,... | |
| Bernard Marks - Geometry - 1871 - 172 pages
...the 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 of the one equal... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...angle BAC must be greater than the angle EDF. Therefore, if two triangles, &c. PROPOSITION XV. THEOREM. If two triangles have the three sides of the one equal to trie '.hree sides of the other, each to each, the three angles will also be eqi. il, each to each,... | |
| 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, 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... | |
| 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... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...are also equal. (Eucl. i. 6.) PBOP. C. THEOREM. If two triangles have the three sides of the one eqwl to the three sides of the other, each to each, the triangles must be equal in all respects. Let the three sides of the A s ABC, DEF be equal, each to each, that... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...coincide throughout (26, Ax. 12). Thus circles having equal radii are equal ; and triangles having the three sides of the one equal to the three sides of the other, each to each, are also equal. Equal figures are always similar; but similar figures may be very unequal. 175. In... | |
| 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...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, AC to DF, and... | |
| 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... | |
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