 | Charles Davies - Geometry - 1850 - 238 pages
...chord, and the arc AE equal to EB. First. Draw the two radii CA, CB. Then the two triangles A CD, DCS, have the three sides of the one equal to the three sides of the Of the Circle. B other, each to each : viz. AC equal to CB, being radii, AD equal to DB, by hypothesis,... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...contradicts the hypothesis : therefore, BA C is greater than EDF. PROPOSITION X. THEOEEM. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are equal. Let EDF and BAC be two triangles, having the side ED=BA, the... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...EAD will be equal to tho angle K. For, draw the chord DE. Then the two triangles IKL and EAD, having the three sides of the one equal to the three sides of the other, each to each, the angle EAD will be equal to the angle K (Bk. I. Th. viii). PROBLEM 1X. Through a g1ven... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...triangles coincide, and are equal, in all respects, as stated above. COR. Hence, also, if two triangles have the three sides of the one equal to the three sides of the other, each to each, in the same order, the two triangles will be equal, and their angles likewise will be... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...hypothesis : therefore, BA C is greater than EDF. PROPOSITION X. THEOREM. If two triangles have ihe three sides of the one equal to the three sides of the other, each to each, the triangles are equal. Let EDF and BA C be two triangles, having the side ED=BA, the... | |
 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...need the following, which have been before proved, viz : Prop X. (of Legendre). " When 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... | |
 | Charles Davies - Geometry - 1855 - 340 pages
...chord, and the arc AE equal to EB- ^ First- Draw the two radii CA, CBThen the two triangles A CD, DCB, have the three sides of the one equal to the three sides of the *Note- When reference is made from one theorem to another, in the same Book, the number of the theorem... | |
 | William E. Bell - Bridge building - 1857 - 250 pages
...1. The diagonal of a parallelogram divides it into two equal triangles. Cor. 2. When two triangles have the three sides of the one equal to the three sides of the other, the angles opposite the equal sides are also equal, and the triangles themselves are equal. Cor. 3.... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...equal spheres are mutually equilateral, they are equivalent. D Let ABC, DEF be two triangles which have the three sides of the one, equal to the three sides of the other, each to each, viz., AB to DE, AC to DF, and BC to EF ; then will the triangle ABC be equivalent to... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...be subtended by the greater side, and the lesser angle by the lesser side. Any two triangles having the three sides of the one equal to the three sides of the other, are equal, equilateral, and equiangular. Any two triangles having each an equal angle contained by... | |
| |
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. 
