 | 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,... | |
 | 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... | |
 | 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... | |
 | 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
...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... | |
 | Mary W I. Shilleto - 1882 - 418 pages
...to one paper, but to make use of the whole set. (a) 1. 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. From every point of a given line, the lines drawn to each... | |
 | Mathematical association - 1883 - 86 pages
...angle of the other. [By Rule of Conversion.] THEOR. 18. 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... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...consequently equal. QED PROPOSITION VII. 305. Theorem.— Two triangles which have the three sides of the one equal to the three sides of the other, each to each, are equal. DEMONSTRATION. Let ABC and DEF be two triangles, in which AB = DE, AC = DF, and BO = EF.... | |
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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. 
