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" If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.... "
Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ... - Page 28
by George Roberts Perkins - 1856 - 235 pages
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...the equal angles lie opposite the equal sides. ELEMENTS OF PLANE GEOMETRY. THEOREM XXVII. 89. If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side is in the triangle having the...
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Elements of Plane and Spherical Trigonometry with Logarithmic and Other ...

Simon Newcomb - Trigonometry - 1882 - 372 pages
...Altitude A = b sin y. Therefore, a being the base, "/ ' Area = \ah = \ab sin y. QED Cor. 1. If two triangles have two sides of the one respectively equal to two sides of the other, and the angles which these sides form supplementary, the triangles will be equal in area. For the sines of...
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Gibson's London matriculation guide, by J. Gibson [and others].

1882 - 376 pages
...Ans.—2112. GEOMETRY. Examiners—Prof. AG GREENHILL, MA, and BENJAMIN WILLIAMSON, Esq., MA, FRS 1. If two triangles have two sides of the one respectively equal to two sides of the other, but the contained angle of the one greater than the contained angle of the other, prove that the base...
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 354 pages
...triangles, the equal angles lie opposite the equal sides. PROPOSITION VIII. 307. Theorem.— If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side belongs to the triangle having...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...construction as in the text, but let A DEO fall on the other side of DE. PROPOSITION 25. THEOREM. If two triangles have two sides of the one respectively equal to two sides of the other, but their bases unequal, the angle contained by the two sides of the triangle which has the greater...
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Report of the School Committee of the City of Providence, Presented to the ...

Public schools - 1884
...Prove that if two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. 8. Prove that if the...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...opposite equal sides are equal.) But BDA -f 2 ^C = st. , = st. :. 178. COROLLARY I. If two triangles have two sides of the one respectively equal to two sides of the other, and the angles opposite to one pair of equal sides equal, then, if one of the angles opposite the other pair...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...THEOREM. 86. If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second. In the triangles ABC and DEF, let the side AB be equal...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...angles opposite equal sides are equal.) But BDA + 4 BDC = st. , = st. . 178. COROLLARY I. If two triangles have two sides of the one respectively equal to two sides of the other, and the angles opposite to one pair of equal sides equal, then, if one of the angles opposite the other pair...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 332 pages
...k IS EXERCISES ON BOOK IV. -f ( • ' \ [-:-" u3 THEOREMS. 1. Two" triangles are equivalent if they have two sides of the . one respectively equal to...sides of the other, and the included angle of the one equal to the supplement of the included angle of the other. 2. The two opposite triangles formed...
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