 | William E. Bell - Bridges - 1859 - 226 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 arc equal. Cor. 3.... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...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
...to PC (BI, T. XII.); consequently the oblique lines AB, AC are equal, and the two triangles ADB, ADC have the three sides of the one equal to the three sides of the other; therefore they are equal (BI, T. XXV.), and the angle ADB = ADC; hence each is a right angle, and AD... | |
 | 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
...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... | |
 | Benjamin Greenleaf - Geometry - 1866 - 328 pages
...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... | |
 | Charles Davies - Mathematics - 1867 - 186 pages
...need the following, which have been before proved ; viz. : Prop. X. (of Legendre). "If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles will be equal in all their parts." Prop. V. " If two triangles have two... | |
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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. 
