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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...: Translated from the French for the Use of the ... - Σελίδα 9
των Adrien Marie Legendre, John Farrar - 1825 - 224 σελίδες
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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. Ci» For if the triangle DEF be...

## A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - 1816 - 294 σελίδες
...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,...

## Elements of Geometry

Adrien Marie Legendre - 1819 - 208 σελίδες
...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...

## Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 224 σελίδες
...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...

## 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...

## Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - 1829 - 172 σελίδες
...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...

## A concise system of mathematics

Alexander Ingram - 1830 - 120 σελίδες
...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...

## Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 σελίδες
...the three angles of the one equal to the three angles of the other, each to each, they shall likewise have the three sides of the one equal to the three sides of the othrr, each to each, viz. those which are opposite to the equal angles.* Let the spherical triangles...

## Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...and С с ; draw P О perpendicular to Ce; and join OQ. Then, because the triangles С P с, С Q с have the three sides of the one equal to the three sides scribe two circles, and kt them cut one another in P; and from P draw PM perpendicular to А В : then...

## Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 359 σελίδες
...contradicts the hypothesis: therefore, BAC 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 three angles will also b« equal, each to each, and the triangles themselves will be equal. Let...