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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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Texas School Journal, Volume 8

Education - 1890
...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...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
...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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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 354 pages
...triangles coincide, and are consequently equal. QED PROPOSITION VII. 305. Theorem.— Two triangles which have the three sides of the one equal to the three sides of the other, each to each, are equal. DEMONSTRATION. Let ABC and DEF be two triangles, in which AB = DE, AC = DF, and BO = EF....
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1883
...sides which subttnd them are also equal. (Kucl. I. 6.) SE PROPOSITION C. THEOREM. If two triangles ham the three sides of the one equal to the three sides of the otlwr, each to each, the triangles must be equal in all respects. Let the three sides of the A s ABC,...
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Yale Examination Papers

F. B. Stevens - Examinations - 1884 - 202 pages
...trapezoid is equal to the product of its altitude and half the sum of its parallel sides. (LOOMIS.) 1. If two triangles have the three sides of the one equal...each, and the triangles themselves will be equal. 2. Two parallels intercept equal arcs on a circumference. 3. In any triangle, if a straight Hue is...
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The elements of plane geometry, Volume 1

Mathematical association - 1884
...less than AC and AD is drawn to D the middle point of BC, shew that the angle ADB is acute. THEOK. 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 angrles those are equal which are opposite to...
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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...less than AC and AD is drawn to D the middle point of BC, shew that the angle ADB is acute. 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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Journal of the Board of Education of the City of New York

New York (N.Y.). Board of Education - Education - 1885 - 990 pages
...side and two adjacent angles in the other, each to each, the two triangles are equal in all respects. If two triangles have the three sides of the one equal...to the three sides of the other, each to each, the two triangles are equal, and the equal angles are opposite the equal sides. If two sides of a triangle...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1885 - 540 pages
...DF, and BC greater than EF, then is the angle BAC greater than the angle EDF. PROPOSITION X. THEOREM. 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 in all respects. In the triangles ABC and DEF, let AB be equal to DE, AC to DF,...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 346 pages
...former is called a direct, and the latter an indirect demonstration. THEOREM VIII. If two tnangles have the three sides of the one equal to the three...sides of the other, each to each, the three angles wiU also be equal, each to each. Let the two triangles ABC, ABD, have the side AB equal to the side...
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