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" Two triangles are equal if the three sides of the one are equal, respectively, to the three sides of the other. In the triangles ABC and A'B'C', let AB be equal to A'B', AC to A'C', BC to B'C'. To prove that A ABC = A A'B'C'. "
Elements of Plane and Solid Geometry - Page 44
by George Albert Wentworth - 1877 - 398 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...therefore, taking away the equal quantities, AG, AB, we shall have GC < BC, or EF< BC. THEOREM. 43. Two triangles are equal, when the three sides of the one are equal to the three sides of the other, each to each. Demonstration. Let the side AB = DE (Jig. 23), AC =...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...these results contradict the hypothesis; therefore, BAC is greater than EDF. PROPOSITION XI. THEOREM. Two triangles are equal, when the three sides of the one are respectively equal to the three sides of the other. LET the side AB (see the diagram of Prop. 6.) be...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...therefore, taking away the equal quantities, AG, AB, we shall have GC < BC, or EF<BC. , . THEOREM. / / 43. Two triangles are equal, when the three sides of the one are equal to the three sides of the other, each to each. Demonstration. Let the side AB = DE (Jig, 23,) AC -...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 pages
...therefore, taking away the equal quantities, AG, AB, we shall have GC < BC, or EF<BC. THEOREM. 43. 7\ťo triangles are equal, when the three sides of the one are equal to the three sides of the other, each to each. Demonstration. Let the side AB = DE (fig. 23,) AC -...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...therefore, taking away the equal quantities, AG, AB, we shall have GC <[ BC, or EF<BC. THEOREM. 43. 7V0o triangles are equal, when the three sides of the one are '< equal to the three sides of the other, each to each. Demonstration. Let the side AB = DE (fig. 23,) JtC =...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 246 pages
...bdc, you will be able to find out another instance of the equality of triangles. What is it ? P. — Two triangles are equal when the three sides of the one are equal to the three sides of the other, each to each. M. — Right; and what angles are equal in two such...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 254 pages
...bdc, you will be able to find out another instance of the equality of triangles. What is it ? P.—Two triangles are equal when the three sides of the one are equal to the three sides of the other, each to each. M.—Right; and what angles are equal in two such triangles...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 235 pages
...BC(4l); therefore, taking away the equal quantities, AG, AB, we shall have GC<^BC, or EF<BC. THEOREM. 43. Two triangles are equal, when the three sides of the one are equal to the three sides of the other, each to each. Demonstration. Let the side AB = DE (fig. 23),AC = DF,...
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry, Modern - 1864 - 292 pages
...necessary, and they are generally enough, to determine the triangle. THREE SIDES EQUAL. 282. Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. Let the side BD be equal to AI, the side BC equal...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 432 pages
...necessary, and they are generally enough, to determine the triangle. THREE SIDES EQUAL. 282. Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. Let the side BD be equal to AI, the side BC equal...
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