| William E. Bell - Bridges - 1859 - 226 pages
...are equal. Cor. 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
...(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 triangles, as ABC... | |
| 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... | |
| Elias Loomis - Conic sections - 1860 - 246 pages
...BAC must be greater than the angle EDF. Therefore, if two triangles, &c. PROPOSITION XV. THEOREM. v -If two triangles have the three sides of the one equal to trie three sides of the other, each to each, the three angles will also be equal, each to each, and... | |
| 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
...equal spheres, are mutually equilateral, they are equivalent. £et ABC, DEF be two triangles, having the three sides of the one equal to the three sides of the other, each to each, namely, А В to DE, AC to DF, and С В to EF; then their triangles will be equivalent. Let 0 be the... | |
| 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 he the pole of... | |
| 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 angle E 0 G (Prop.... | |
| 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 angle E 0 G (Prop.... | |
| Charles Davies - 1863 - 436 pages
...latter an indirect demonstrationTHEOREM VIllIf two triangles have the three sides of the one eqvai to the, three sides of the other, each to each, the three angles will equal, each to eachLet the two triangles ABC, ABD, have the side AB equal to the side AB, the side... | |
| |