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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 21
by Adrien Marie Legendre - 1825 - 224 pages

An essay on mechanical geometry, explanatory of a set of models

Benjamin Donne - 1796 - 120 pages
...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...

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

Daniel Cresswell - Geometry - 1816 - 352 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,...

Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...will be equal to the arc EJVG. For, if the radii CD, OG, be drawn, the two triangles ACD, EOG, will have the three sides of the one equal to the three sides of the other, each to each, namely, AC = EO, CD= OG and AD = EG; therefore these triangles are equal (43); hence the angle ACD...

Elements of Geometry

Adrien Marie Legendre - 1825 - 570 pages
...compare thp triangle ADO with the triangle COB, we find the side AD = CB, and the angle ADO = CBO (67) : also the angle DAO = OCB ; therefore these two triangles...diagonals of a rhombus cut each other mutually at right unglos. i SECTION SECOND. Of the Circle and the Measure of Angles. DEFINITIONS. ^0. THE circumference...

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

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 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...

Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...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 - Geometry - 1829 - 218 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...

A Concise System of Mathematics ...

Alexander Ingram - Mathematics - 1830 - 458 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...