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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. "
Principles of Plane Geometry - Page 13
by James Wallace MacDonald - 1889 - 63 pages
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...and consequently, AE is equal to BF. Hence, the two triangles ACE and BDF have the three sides of the one equal to the three sides of the other, each to each, and therefore the angle ACE is equal to the angle BDF (Bk. I. Th. viii). THEOREM XII. BOOK V , Of Planes....
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 238 pages
...and consequently, AE is equal to BF. Hence, the two triangles ACE and BDF have the three sides of the one equal to the three sides of the other, each to each, and therefore the angle A CE is equal to the angle BDF (Bk. I. Th. viii). THEOREM XII. 1:21 Of Plane*....
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Elements of Geometry and Trigonometry

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 the side DF=AC; then will...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

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 draw...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

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, and the side DF=AC; then...
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Elements of geometry and mensuration

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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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

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. V....
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1855 - 340 pages
...consequently, AE is equal to BF- Hence, the two triangles ACE and BDF have the' three sides of the one equal to the three sides of the other, each to each, and therefore the angle ACE is equal to the angle BDF (Bk- I- Th- viii)- \ THEOREM XII121 BOOK V Of...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...therefore, BA C 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 triangles are equal. Let EDF and BAC be two triangles, having the side ED=BA, the side EF=BC, and the side DF=AC\ then will...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...given lines, any two of which are greater than the third, to make a triangle. DEMONSTRATION. — P. 8. If two triangles have the three sides of one equal to the three sides of another, each to each, the angle contained by two equal and conterminous sides of the one, shall be...
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