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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
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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
...unequal,; the base of that 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
...with AB, shew that AC 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 to...
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Elementary geometry

James Maurice Wilson - 1878
...and HF together are 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
...triangle be equal, the 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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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1879
...by a process like that in Prop. A, we can prove the following theorem : PROPOSITION C. THEOREM. // 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. Let the three sides of the A s ABC, DEF be equal, each to...
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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...
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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
...and therefore this 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

Simon Newcomb - Geometry - 1881 - 418 pages
...equal (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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The Oxford examiner, ed. by M.W.I. Shilleto, Issues 1-5

Mary W I. Shilleto - 1882
...students are advised not to confine themselves to one paper, but to make use of the whole set. (a) 1. 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. From every point of a given line, the lines drawn to each...
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Class lessons on Euclid

Marianne Nops - 1882
...proposition. SUMMARY OP PROPOSITION VIII., THEOREM 5. If in two triangles the, three sides of one are equal to the three sides of the other each to each, the triangles are equal in all respects. Cons.— Nil. AAA Proof. — By superposition. If the triangles...
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