| Adrien Marie Legendre - Geometry - 1874 - 500 pages
...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, AC to DF, and... | |
| Benjamin Greenleaf - Geometry - 1874 - 206 pages
...(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... | |
| B. Marks - 1875 - 176 pages
...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... | |
| Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...also equal. (Eucl. I. 6.) SB * PROPOSITION 0. THEOREM. 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. JS~ OS Let the three sides of the A s ABC, DEF be equal, each to each,... | |
| Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...angle being greater than the base of the other. THEOR. 15. If two triangles have the three sides of the **one equal to the three sides of the other, each to each,** then the triangles are identically equal, and of the angles [Alternative proofs, (i) by Theors. 14... | |
| Elias Loomis - Conic sections - 1877 - 458 pages
...Therefore, if two triangles, etc. PROPOSITION XV. TIIEOREM. If two triangles have the three sides of the **one equal to the three sides of the other, each to each, the** three angles will also be equal, each to each, and the triangles themselves will be equal. Let ABC,DEFbe... | |
| Euclides - 1877 - 58 pages
...make equal angles with AB. PROPOSITION VIII. THEOREM. If two triangles have the three sides of the **one equal to the three sides of the other, each to each ; the** two triangles shall be equal in all respects. Let ABC, DEF be two triangles, in which AB is equal to... | |
| James Maurice Wilson - 1878 - 450 pages
...therefore EG or BC is greater than EF. QED THEOREM 15. If two triangles have the three sides of the **one equal to the three sides of the other, each to each,** then the triangles are identically equal, and of the angles those are equal which are opposite to equal... | |
| Isaac Sharpless - Geometry - 1879 - 282 pages
...from A to the middle of the base D an arc of a great circle. Then the two triangles ADB, ADC, having **the three sides of one equal to the three sides of the other,** are equal (IX. 9) in all their parts; hence the angle ABD is equal to the angle A CD. Conversely, if... | |
| Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...Wherefore, Upon the same base, QED PROP. VIII. THEOREM. If two triangles have the three sides of the **one equal to the three sides of the other, each to each,** then the angle which is contained by any two sides of the one triangle shall be equal to the angle... | |
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