 | Euclides - 1874 - 120 pages
...so 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... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...to the 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... | |
 | B. Marks - 1875 - 176 pages
...angle c, opposite the side A B. 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... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...the base of that which has the greater 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)... | |
 | Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...be equal, the sides which subtend them are 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,... | |
 | Euclides - 1877 - 58 pages
...AB, shew that AC and BD are also equal and 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... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...must be greater than the angle EDF. 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... | |
 | Euclides - 1878 - 398 pages
...be equal, the sides which subttnd them are also equal. (Bucl. I. 6.) SE PROPOSITION C. THEOREM. If two triangles have the three sides of the one equal to the three sides of the otlwr, each to each, the triangles must be equal in all respeett. Let the three sides of the A s ABC,... | |
 | Universities and colleges - 1879 - 88 pages
...figure. What are similar figures? Name the classes of quadrilaterals. Prove that two triangles with the three sides of the one equal to the three sides of the other, each to each, are equal. Prove that the three angles of a triangle are equal to two right angles. Prove... | |
 | Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...therefore this case is to be dismissed. 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... | |
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If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent. 
