 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...the arcs AD, EG will be equal. For, if the radii CD, OG are drawn, the triangles AC D, EOG, having the three sides of the one equal to the three sides of the other, each to each, are themselves equal (Theo. XIII. Bk. I. ) ; therefore the angle ACD is equal to the angle EOG (Theo.... | |
 | 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... | |
 | 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... | |
 | Benjamin Greenleaf - Geometry - 1875 - 204 pages
...been shown that is not equal 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...triangles themselves will be equal. Let the triangles ABC, DBF have the side AB equal to DE, AC to DF, and BC to EF; then will the angle A be equal to D, the... | |
 | 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 the one equal... | |
 | Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...triangle 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...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
...unequal,; 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) by Theors. 14... | |
 | Euclides - 1877 - 58 pages
...with 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 which AB is equal to... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...BAC 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 be equal. Let ABC,DEFbe... | |
 | James Maurice Wilson - 1878 - 450 pages
...and HF together are greater than EF; (Th. 12.) 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... | |
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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. 
