| Bernhard Marks - Geometry - 1869 - 172 pages
...THEOREMS ILLUSTRATED. 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... | |
| Charles Davies - Geometry - 1870 - 392 pages
...called a direct, and the latter an indirect demonstration. THEOREM via. If two triangles have tlie three sides of the one equal to the three sides of the other, each to each, the three angles will aho be equal, each to each. Let the two triangles ABC, ABD, have the side AB... | |
| Euclides - 1871 - 136 pages
...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, DEF be equal,... | |
| 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... | |
| 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 - 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... | |
| 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... | |
| Thomas Steadman Aldis - 1872 - 84 pages
...can prove that XR is equal to PR. Then in the triangles PQR and XQR the three sides of the one are equal to the three sides of the other, each to each, therefore their angles are equal, each to each. [A. XI But the angles of the triangle ABC are equal to those... | |
| 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... | |
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