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" If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects. "
Mathematics, mechanics, heat - Page 21
by American School (Chicago, Ill.) - 1903
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 262 pages
...produced, the exterior angle is equal to the sum of the two interior and opposite. THEOREM VIII. 40, If two triangles have two sides and the included angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in...
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...produced, the exterior angle is equal to the sum of the two interior and opposite. THEOREM VIII. 40. If two triangles have two sides and the included angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...(A. 8). Hence, CB must be the prolongation of AC ; which was to be proved. PROPOSITION Y. THEOREM. If two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each, the triangles will be equal in att...
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First Lessons in Geometry: In Two Parts

B. Marks - 1875 - 176 pages
...What do you think of the areas of the triangles ? a d I cef DEMONSTRATION. We wish to prove, that, // two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 426 pages
...adj. A equal, each Zis a rt. ¿ ). a ED PROPOSITION XLIV. THEOREM. 140. Two parallelograms, having two sides and the included angle of the one equal respectively to two sides and the included angle of the other, are equal in all respects. B СВ' С' A -------- DA, In the parallelograms AB С D and...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...together be equal to the sum of all the angles BAC, CAD, etc., formed about A. PROPOSITION VI. THEOREM. If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to •each, the two triangles will be equal,...
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Elements of Plane Geometry, Part 1

Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...AF and FE are also equal (const.), and the angles AFC and EFB are equal (Prop. XVII.). Therefore the two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each, and are every way equal (Prop. IV.);...
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...adj. /a equal, each Лis a rt. Z ). QED PROPOSITION XLIV. THEOREM. 140. Two parallelograms, having two sides and the included angle of the one equal respectively to two sides and the included angle of the other, are equal in all respects. B CD О A DA' 111 the parallelograms AB С D and A' B' C'...
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 418 pages
...9) Or, because QU= QW (I.), TQ+QU= TU> TW. 6. Comparing with (4), TU> TV. QED 45 THEOREM XIX. 108. If two triangles .have two sides and the included angle of the one equal to two sides and the included angle of the other, they are identically equal. Hypothesis. ABC&n&MNP,...
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...and ED take the direction BC; then EF will take the direction BH, and ABH = ABC + DEF. THEOREM IV. If two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each, the triangles will be equal in all...
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