 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.  Elements of Geometry - Page 9by Adrien Marie Legendre - 1825 - 224 pagesFull view - About this book
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...contradicts the hypothesis: therefore, BAC is greater than EDF. PROPOSITION X. THEOREM. If 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 b« equal, each to each, and the triangles themselves will be equal. Let... | |
 | John Playfair - Geometry - 1836 - 148 pages
...proved. COR. Hence, every equiangular triangle is also equilateral. PROP. VII. THEOR. If two triangles have the three sides of the one equal to the three sides of the other, each to each ; the angles opposite the equal sides are also equal. Let the two triangles ABC, DEF, have the three... | |
 | Euclides - 1840 - 192 pages
...agree in having two sides, and the angle contained by those sides, equal (as in Prop. 4); or, in having the three sides of the one equal to the three sides of the other (as in Prop. 8) ; or, finally, in having two angles and a side, similarly placed with respect to the... | |
 | Dionysius Lardner - Curves, Plane - 1840 - 386 pages
...different forms. This proposition is usually enounced thus : — If two triangles have the three sides of one equal to the three sides of the other each to each, then the three angles will le equal each to each, and their areas will be equal. (63.) When two sides... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...: FG ; but, by hypothesis, BC : EF : : AC : DF; consequently FG =DF; hence the triangles EGF, DEF, have the three sides of the one equal to the three sides of the other, each to each ; they are therefore equal (43). But, by construction, the triangle EGF is equiangular with the triangle... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...are equal (Def. 4), therefore AD=DB (BI Prop. 19, Cor. 2); hence the two triangles ACD, BCD, having the three sides of the one equal to the three sides of the other, are equal, (B. I. Prop. 22), and the angles ACD, BCD, are equal ; and therefore the arcs AE, EB,are... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...AP, since PB = PC, the oblique line AB = AC (B. VI, Prop, v) ; therefore the two triangles ADB, ADC have the three sides of the one equal to the three sides of the other ; consequently they are equal (BI, Prop, vm), and the angle ADB is equal to ADC ; therefore each is... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...equal, each to each, and the triangles themselves will be equal. Let ABC, DBF be two triangles having the three sides of the one equal to the three sides of the other, viz.: AB equal to DE, BC to EF, and AC to DF ; then will the three angles also be equal, viz.: the... | |
 | Charles Davies - Logic - 1850 - 398 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 be equal." Prop.... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...AP, since PB = PC, the oblique line AB = AC, (B. VI, Prop. v;) therefore the two triangles ADB, ADC have the three sides of the one equal to the three sides of the other; consequently they are equal, (B. I, Prop, viu,) and the angle ADB is equal to ADC ; therefore each... | |
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