 | Dionysius Lardner - Curves, Plane - 1840 - 386 pages
...admit of two 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
...AT) be drawn to the middle of the base, the two triangles ABD, ADC, will have the three sides of the one equal to the three sides of the other, each to each, namely, AD common, BD = DC,AB = AC; consequently, by the preceding theorem, the two triangles will... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...Therefore, if two triangles, &c. PROPOSITION XV. 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 be equal, each to each, and the triangles themselves will be equal. Let... | |
 | Charles Davies - Logic - 1850 - 398 pages
...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.... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...angle K. For, draw the chord DE. Then the two triangles IKL and EAD, having the three sides of the one equal to the three sides of the other, each to each, the angle EAD will be equal to the angle K (Bk. I. Th. viii). PROBLEM IX. Through a given point to... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...and the latter a negative demonstration. THEOREM VIII. 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 bt equal, each to each. Let the two triangles ABC, ABD, have the side AB... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...therefore, BA C is greater than EDF. PROPOSITION X. THEOEEM. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are equal. Let EDF and BAC be two triangles, having the side ED=BA, the side EF^BC, and... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...angle K. For, draw the chord DE. Then the two triangles IKL and EAD, having the three sides of the one equal to the three sides of the other, each to each, the angle EAD will be equal to the angle K (Bk. I. Th. viii). PROBLEM 1X. Through a g1ven po1nt to... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...therefore, BA C is greater than EDF. PROPOSITION X. THEOREM. If two triangles have ihe three sides of the one equal to the three sides of the other, each to each, the triangles are equal. Let EDF and BA C be two triangles, having the side ED=BA, the side EF=BC,... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...equal, in all respects, as stated above. COR. Hence, also, if two triangles have the three sides of the one equal to the three sides of the other, each to each, in the same order, the two triangles will be equal, and their angles likewise will be equal, each to... | |
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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. 
