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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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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 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, vin.) If two of the given lines are equal, the triangle will be isosceles; when...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...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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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 236 pages
...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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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 334 pages
...angle 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 Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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 mensuration

Thomas Lund - Geometry - 1854 - 192 pages
...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 - Mathematics - 1855 - 630 pages
...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 - 336 pages
...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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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...equal, as in the case of a rhombus, we have AB — AD, and the two triangles AEB and AED will have the three sides of the one equal to the three sides of the other respectively, consequently they will be equal (T. XXV.), and the angle AEB = AED, that is, in a rhombus...
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