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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.
Principles of Plane Geometry - Page 13
by James Wallace MacDonald - 1889 - 63 pages

## Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...throughout. Thus, two circles having equal radii are equal ; and two triangles, having the three sides of the one equal to the three sides of the other, each to each, are also equal. 2. Equivalent figures are such as contain equal areas. Two figures may be equivalent,...

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

Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...between any two sidei of a triangle, etc. THEOREM XXI. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the two triangles are eqml, and the equal angles are opposite the equal sides. In two triangles, as ABC...

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

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...equal. For, if the radii CD, OG are drawn, the triangles А С D, EOG, 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 А С D is equal to the angle EOG...

## Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...are equivalent. ELEMENTS OF GEOMETRY. Let ABC, DEF be two triangles, having the three sides of the one equal to the three sides of the other, each to each, namely, AB to DE, AC to DF, andCBtoEF; then their triangles will be equivalent. Let 0 he the pole of...

## Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
.... — THEOREM . ELEMENTS OF GEOMETRY. Let ABC, DEF be two triangles, having the three sides of the one equal to the three sides of the other, each to each, namely, AB to DE, AC toDF, andCB toEF; then their triangles will be equivalent. Let 0 be the pole of...

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

Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...= 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
...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 DP, and BC...

## Outlines of Mathematical Science for the School Room

Charles Davies - Mathematics - 1867 - 186 pages
...have been before proved ; viz. : Prop. X. (of Legendre). "If two triangles have the three sides of the one equal 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 angle...