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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 - Page 9
by Adrien Marie Legendre - 1841 - 235 pages
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An essay on mechanical geometry, explanatory of a set of models

Benjamin Donne - 1796
...the line DF will coincide with AC, and EF with BC. THEOREM 16. If two triangles have three sides of one equal to the three sides of the other, each to each, thefe triangles are equal in every rcfpeft. — 8 E. 1, or 17 D. 1. Ciť For if the triangle DEF be...
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 294 pages
...which are equal to them, are equal to one another. (2l6.) COR. 2. Hence, if two spherical triangles have the three sides of the one equal to the three sides of the other, or two sides and the included angle in the one, equal to two sides and the included angle, in the other,...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...FG ; 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 Geometry

Adrien Marie Legendre - 1825 - 224 pages
...angles opposite to the equal sides are equal. Demonstration. Let the side AB = AC (fig. 28), then will the angle C be equal to B. Draw the straight line...also equiangular, that is, it has its angles equal. 47. Scholium. From the equality of the triangles ABD, ACD, it follows, that the angle BAD— DAC, and...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...to the equal sides are equal. Demonstration. Let the side AB = AC (fig. 28), then will the Fig.;28. angle C be equal to B. Draw the straight line AD from...sides of the one, equal to the three sides of the qther, each to each, namely, AD common to both, AB — AC, by hypothesis, and BD = DC, by construction...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...the figure will be a parallelogram. Demonstration. Draw the diagonal BD ; the two triangles ABD, BDC, have the three sides of the one equal to the three sides of the other, each to each, they are therefore equal, and the angle ADB opposite to the side AB is equal to the angle DBC opposite...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...however dissimilar ; thus a circle may be equivalent to a square, a triangle to a rectangle, &c. having the three sides of the one equal to the three sides of the other, each to each, are also equal. 162. Two figures are similar, which have the angles of the one equal to the angles...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...base at right angles. OF GEOMETRY. Book I. s Sup. PROP. IV. THEOREM. If two triangles, ABC and DEF, have the three sides of the one equal to the three sides of the other, each to each, viif. AB to DE, AC to DF, and BC to EF, the triangles are equal in every respect. Let AB be that side...
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 172 pages
...their parts ; they are not different, therefore, but equal; and we say, universally, When two triangles have the three' sides of the one equal to the three sides of the other respectively, the angles will also be equal, respectively, and the two triangles will be equal in all...
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A concise system of mathematics

Alexander Ingram - Mathematics - 1830 - 120 pages
...one and the same great circle, meet in the poles of that circle. PROP. V. If two spherical triangles have the three sides of the one equal to the three sides of the other, each to each, the angles which are opposite to the equal sides are likewise equal ; and conversely. PROP. VI. If...
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