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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 and Trigonometry: With Applications in Mensuration - Page 59
by Charles Davies - 1886 - 324 pages
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Elementary geometry

James Maurice Wilson - 1878 - 450 pages
...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, James Hamblin Smith - Geometry - 1878 - 398 pages
...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 - 88 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

Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 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 - 380 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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The Oxford examiner, ed. by M.W.I. Shilleto, Issues 1-5

Mary W I. Shilleto - 1882 - 418 pages
...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 - 278 pages
...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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Texas School Journal, Volume 8

Education - 1890 - 384 pages
...surface or solid) and a mathematical figure (as area or volume). 3. Prove that if two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are equal. 4. Jf the area of a triangle, whose shortest side is six feet, is 4 .4 square...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883 - 86 pages
...being greater than the angle of the other. [By Rule of Conversion.] THEOR. 18. 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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