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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, After Legendre, with a Selection of Geometrical ... - Page 45
by Charles Scott Venable - 1881
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The Logic and Utility of Mathematics,: With the Best Methods of Instruction ...

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....
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Elements of Geometry: With, Practical Applications

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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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 238 pages
...chord, and the arc AE equal to EB. First. Draw the two radii CA, CB. Then the two triangles A CD, DCS, have the three sides of the one equal to the three sides of the Of the Circle. B other, each to each : viz. AC equal to CB, being radii, AD equal to DB, by hypothesis,...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...chord, and the arc AE equal to EB. First. Draw the two radii CA, CB. Then the two triangles A CD, DCB, have the three sides of the one equal to the three sides of the *Note. When reference is made from one theorem to another, in the same Book, the number of the theorem...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...contradicts the hypothesis : 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...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 340 pages
...EAD will be equal to tho 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...
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Elements of geometry and mensuration

Thomas Lund - Geometry - 1854 - 522 pages
...triangles coincide, and are 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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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...hypothesis : 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,...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Electronic book - 1855 - 592 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 bo equal." Prop....
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1855 - 340 pages
...chord, and the arc AE equal to EB- ^ First- Draw the two radii CA, CBThen the two triangles A CD, DCB, have the three sides of the one equal to the three sides of the *Note- When reference is made from one theorem to another, in the same Book, the number of the theorem...
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