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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, Conic Sections, and Plane Trigonometry - Page 27
by Elias Loomis - 1877 - 443 pages

## Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 628 pages
...arcs AD, EG will be equal. For, if the radii CD, 0 G are drawn, the triangles ACD, E 0 G, having tlffe three sides of the one equal to the three sides of the other, each to each, are themselves equal (Prop. XVIII. Bk. I.) ; therefore the angle ACD is equal to the angle E 0 G (Prop....

## Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 320 pages
...the arcs AD, EG will be equal. For, if the radii CD, 0 G are drawn, the triangles ACD, E 0 G, having the three sides of the one equal to the three sides of the other, each to each, are themselves equal (Prop. XVIII. Bk. I.) ; therefore the angle ACD is equal to the angle E 0 G (Prop....

## Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - 1863 - 424 pages
...latter an indirect demonstrationTHEOREM VIllIf two triangles have the three sides of the one eqvai to the, three sides of the other, each to each, the three angles will equal, each to eachLet the two triangles ABC, ABD, have the side AB equal to the side AB, the side...

## Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1864 - 330 pages
...latter an indirect demonstrationTHEOREM VIIIIf two triangles have the three sides of the one cqva* to the, three sides of the other, each to each, the three angles wil! al *1 гл equal, each to eachLet the two triangles ABC, ABD, have the side AB equal to the side...

## Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1865 - 592 pages
...need the following, which have been before proved, viz : Prop X. (of Legendre). " When two triansles have the three sides of the one equal to the three...equal, each to each and the triangles themselves will bo eqoa.." Prop. V. " When two triangles have two sides, and the included angle of the one equal to...

## Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Conic sections - 1865 - 472 pages
...remain ED = CF, (Ax. 3) ; but BE = AC, and AF = BD, (Th. 24); hence we have two A's, CAF and EBD, which have the three sides of the one equal to the three sides of the other, e,ach to each; therefore, the two A's are equal, (Th. 21). If, from the whole figure ABDC, we take away the A CAF,...

## Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1866 - 328 pages
...equal to it ; hence the angle A must be greater than the angle D. PROPOSITION XVIII. — THEOREM. 80. If two triangles have the three sides of the one equal...to the three sides of the other, each to each, the triangles themselves will be equal. Let the triangles ABC, DEF have the side AB equal to DE, AC to...

## Outlines of Mathematical Science for the School Room

Charles Davies - Mathematics - 1867 - 186 pages
...proposition, we need the following, which have been before proved ; viz. : Prop. X. (of Legendre). "If two triangles have the three sides of the one...to the three sides of the other, each to each, the triangles will be equal in all their parts." Prop. V. " If two triangles have two sides and the included...