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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: With Practical Applications to Mensuration - Page 59
by Benjamin Greenleaf - 1863 - 320 pages
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First Lessons in Geometry: In Two Parts

B. Marks - 1875 - 176 pages
...side A B. DB PROPOSITION XIX. THEOREM. DEMONSTRATION. We wish to prove that, If two triangles have the three sides of the one equal to the three sides of the other, each to each, they are equal in all their parts. Let the two triangles ABC, ADC, have the side AB of the one equal...
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Elements of Geometry Containing Books I. to VI. and Portions of Books XI ...

James Hamblin Smith - Geometry - 1876 - 376 pages
...which subtend them are also equal. (Eucl. I. 6.) SB * PROPOSITION 0. THEOREM. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles must be equal in all respects. JS~ OS Let the three sides of the A s ABC, DEF be equal,...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...which has the greater angle being greater than the base of the other. THEOR. 15. If two triangles have the three sides of the one equal to the three sides of the other, each to each, then the triangles are identically equal, and of the angles [Alternative proofs, (i) by Theors. 14...
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Euclid, book i., propositions i. to xxvi., with exercises and alternative ...

Euclides - 1877
...and BD are also equal and make equal angles with AB. PROPOSITION VIII. THEOREM. If two triangles have the three sides of the one equal to the three sides of the other, each to each ; the two triangles shall be equal in all respects. Let ABC, DEF be two triangles, in which AB is equal...
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Elementary geometry

James Maurice Wilson - 1878
...greater than EF; (Th. 12.) therefore EG or BC is greater than EF. QED THEOREM 15. If two triangles have the three sides of the one equal to the three sides of the other, each to each, then the triangles are identically equal, and of the angles those are equal which are opposite to equal...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides - 1878
...sides which subttnd them are also equal. (Bucl. I. 6.) SE PROPOSITION C. THEOREM. If two triangles have the three sides of the one equal to the three sides of the otlwr, each to each, the triangles must be equal in all respeett. Let the three sides of the A s ABC,...
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A Hand-book of Requirements for Admission to the Colleges of the United ...

Universities and colleges - 1879 - 86 pages
...figure. What are similar figures? Name the classes of quadrilaterals. Prove that two triangles with the three sides of the one equal to the three sides of the other, each to each, are equal. Prove that the three angles of a triangle are equal to two right angles. Prove that the angle...
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Euclid for beginners, books i. and ii., with simple exercises by F.B. Harvey

Euclid, F. B. Harvey - Geometry - 1880 - 119 pages
...case is to be dismissed. Wherefore, Upon the same base, QED PROP. VIII. THEOREM. If two triangles have the three sides of the one equal to the three sides of the other, each to each, then the angle which is contained by any two sides of the one triangle shall be equal to the angle...
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Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable - 1881 - 382 pages
...THEOREM. .the vertex A, and D, the middle point of the base, BC ; the two triangles ABD, ADC, have the three sides of the one equal to the three sides of the other, each to each ; namely, AD common, AB = AC by hypothesis, and BD = DC by construction ; therefore (by the last Proposition)...
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 418 pages
...(1), 3. Comparing with the last two equations of (1), it is seen that the triangles BFD and AEC have the three sides of the one equal to the three sides of the other. Therefore Triangle A EC = triangle BFD. 4. From the trapezoid ABED take away the triangle A EC, and...
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