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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. "
Elements of Geometry: With Practical Applications to Mensuration - Page 59
by Benjamin Greenleaf - 1863 - 320 pages
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...describe (42.) the equilateral triangle BDC, and join A D. Then, because the triangles AB D, А С D have the three sides of the one equal to the three sides of the other, each to each, (7.) the angle BAD is equal to the angle CAD, Therefore, &c. Cer. By repeating this process with the...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 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 bę equal, each to each, and the triangles themselves will be equal. Let...
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The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...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...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 194 pages
...triangles 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...
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A Treatise on Geometry and Its Application in the Arts

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...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 235 pages
...; 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...
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...these 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...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...will intersect in two points G and H, thus giving two triangles DGF and DHF ; but these two triangles, having the three sides of the one equal to the three sides of the other, are identical (Prop. vm). If two of the given lines are equal, the triangle will be isosceles ; when...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...also be 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...
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The Logic and Utility of Mathematics,: With the Best Methods of Instruction ...

Charles Davies - Logic - 1850 - 375 pages
...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....
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