| Elias Loomis - Geometry - 1871 - 302 pages
...eqi. il, 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 - 566 pages
...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 are... | |
| 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 are... | |
| Euclid, Charles Peter MASON - Geometry - 1872
...equal to each other, the £s opposite to them are also equal. (Prop. V.) Let ABO and DEF be the two As **having the three sides of the one equal to the three sides of the other, each to each.** Let the ADEF be applied to the AABC so that the point D may coincide with the point A, and the line... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...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... | |
| Benjamin Greenleaf - Geometry - 1874 - 206 pages
...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,... | |
| Adrien Marie Legendre - Geometry - 1874 - 512 pages
...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,... | |
| Euclides - 1874 - 234 pages
...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
...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
...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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