 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...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 bo equal." Prop.... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...throughout. Thus, two circles having equal radii are equal ; and two triangles, having the three sides of the one equal to the three sides of the other, each to each, are also equal. 2. Equivalent figures are such as contain equal areas. Two figures may be equivalent,... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...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... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...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 - 1862 - 532 pages
...equal. For, if the radii CD, OG are drawn, the triangles А С D, EOG, 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 А С D is equal to the angle EOG... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
.... — THEOREM . 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 toDF, andCB toEF; then their triangles will be equivalent. Let 0 be the pole of... | |
 | Charles Davies - Mathematics - 1867 - 186 pages
...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 sides and the... | |
 | Education - 1868 - 516 pages
...Rhet. This structure is very often neglected. Examples : "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." The article before one here is improper, because the... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...34, Ax. 14). Thus circles having equal radii are equal ; and triangles having the three sides of the one equal to the three sides of the other, each to each, are also equal. Equal figures are always similar ; but similar figures may be very unequal. BOOK IV.... | |
 | Horatio Nelson Robinson - 1869 - 276 pages
...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, each to each; therefore, the two A's are equal, (Th. 21). If, from the whole figure ABDC, we take away the A CAF,... | |
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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. 
