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

Mathematics - 1835 - 684 pages
...last circle in F ; and join FA, F В. Then, because the triangles ECD, FAB have the three sides of the one equal to the three sides of the other, each to each, (7.) they are equal in every respect, and the angle at A is equal to the angle at C. Therefore, &c....
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The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...equiangular triangle is also equilateral. PROP. VII. THEOR. If two triangles have the three sides of the one equal to the three sides of the other, each to each ; the angles opposite the equal sides are also equal. Let the two triangles ABC, DEF, have the three sides...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...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 bę equal, each to each, and the triangles themselves will be equal. Let the...
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An introduction to the theory ... of plane and spherical trigonometry ...

Thomas Keith - 1839 - 498 pages
...equally obtuse. PROPOSITION VII. (308) In any two spherical triangles, if the three sides of the one be equal to the three sides of the other, each to each, the angles which are opposite to the equal sides wiH be equal. Let ABC be any triangle on the surface of...
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A Treatise on Geometry and Its Application in the Arts

Dionysius Lardner - Curves, Plane - 1840 - 386 pages
...sides, a triangle would admit of two different forms. This proposition is usually enounced thus : — If two triangles have the three sides of one equal to the three sides of the other each to each, then the three angles will le equal each to each, and their areas will be equal. (63.) When two sides...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 pages
...AT) be drawn to the middle of the base, the two triangles ABD, ADC, will have the three sides of the one equal to the three sides of the other, each to each, namely, AD common, BD = DC,AB = AC; consequently, by the preceding theorem, the two triangles will...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...triangle is equilateral. PROP. VII. THEOR. If two triangles have three sides of the one respectively equal to the three sides of the other, each to each, the triangles are equal, and the angles are equal which are opposite to the equal sides. In ^s CBA, CDA, if AB, BC, CA = AD,...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...triangle is equilateral. PROP. VII. THEOR. If two triangles have three sides of the one re-spectively equal to the three sides of the other, each to each, the triangles are equal, and the angles are equal which are opposite to the equal sides. In ^s CBA, CDA, if AB, BC, CA = AD,...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...mutually equilateral, they are equivalent. Let ABC, DEF be two triangles which have the three sides of the one, equal to the three sides of the other, each to each, viz., AB to DE, AC to DF, and BC to EF; then will the triangle ABC be equivalent to the triangle DEF....
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The Logic and Utility of Mathematics,: With the Best Methods of Instruction ...

Charles Davies - Logic - 1850 - 398 pages
...been before proved ; viz. : Prop. X. (of Legendre). "When 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 be equal, each to each, and the triangles themselves will be equal." Prop. V....
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