 | 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... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...(Ax. 5). Hence the theorem ; the difference between any two sidei of a triangle, etc. THEOREM XXI. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the two triangles are eqml, and the equal angles are opposite the equal sides. In two... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...parallelogram are equal, as in the case of a rhombus, we have AB = AD, and the two triangles AEB and AED will have the three sides of the one equal to the three sides of the other respectively, consequently they will be equal (T. XXV.), and the angle AEB = AED, that is, in a rhombus... | |
 | Euclides - 1861 - 464 pages
...make a rectil. ¿. = я rcctil. ¿. DEM. 32, I. — I, VI.; 11, V.; 9, V.; 8, I.— Triangles having the three sides of the one equal to the three sides of the other, have the ¿.s equal which are contained by eq. sides. 4, I. If two д s have each two sides and their... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...to it ; hence the angle A must be greater than the angle D. PROPOSITION XVIII. — THEOREM. 80. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles themselves will be equal. Let the triangles ABC, DEF have the side AB equal... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...mutually equilateral, they are equivalent. ELEMENTS OF GEOMETRY. Let ABC, DEF be two triangles, having the three sides of the one equal to the three sides of the other, each to each, namely, AB to DE, AC to DF, andCBtoEF; then their triangles will be equivalent. Let 0... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...arcs AD, EG will be equal. For, if the radii CD, 0 G are drawn, the triangles ACD, E 0 G, having tlffe three sides of the one equal to the three sides of the other, each to each, are themselves equal (Prop. XVIII. Bk. I.) ; therefore the angle ACD is equal to the... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...the arcs AD, EG will be equal. For, if the radii CD, 0 G are drawn, the triangles ACD, E 0 G, having the three sides of the one equal to the three sides of the other, each to each, are themselves equal (Prop. XVIII. Bk. I.) ; therefore the angle ACD is equal to the... | |
 | Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...remain ED = CF, (Ax. 3) ; but BE = AC, and AF = BD, (Th. 24); hence we have two A's, CAF and EBD, which have the three sides of the one equal to the three sides of the other, e,ach to each; therefore, the two A's are equal, (Th. 21). If, from the whole figure ABDC, we take... | |
 | Charles Davies, William Guy Peck - Mathematics - 1865 - 592 pages
...need the following, which have been before proved, viz : Prop X. (of Legendre). " When two triansles 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 bo... | |
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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. 
