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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. "
New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ... - Page 23
by Benjamin Greenleaf - 1873 - 176 pages
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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
...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 - 376 pages
...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...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 each, that...
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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
...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, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1880 - 452 pages
...BAC must be greater than the angle EDF. Therefore, if two triangles, etc. PROPOSITION XV. THEOREM. If two triangles have the three sides of the one equal to the threo sides of the other, each to each, the three angles will also be equal. each to each, and the...
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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 - 418 pages
...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...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 of two given...
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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 do not coincide...
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Texas School Journal, Volume 8

Education - 1890 - 384 pages
...physical ligure (as 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...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 feet, what...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883 - 86 pages
...has the greater base 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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