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" If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects. "
Elements of Geometry...: Translated from the French for the Use of the ... - Page 142
by Adrien Marie Legendre, John Farrar - 1825 - 224 pages
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 438 pages
...equal sides (594). 773. Corollary The radius being the same, two spherical triangles are equal, 1st. When they have two sides and the included angle of the one respectively equal to those parts of the other, and similarly arranged ; 2d. When they have one side and the adjacent angles...
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Plane - 1870 - 304 pages
...greater than the angle opposite the less (§76). On the equality of triangles. 12. When 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 triangles are equal in all respects (§88 a). 13. When two triangles have two angles...
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 320 pages
...the area of either of these triangles. " PROPOSITION 2. Two parallelograms which have two adjacent sides and the included angle of the one respectively equal to two adjacent sides and the included angle of the other are also equal in area. Fig•. 8. Let ABCD and...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 262 pages
...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 all respects. In the triangles ABC, DEF, let the side...
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...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 all respects. In the triangles ABC, DEF, let the side...
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Treatise on Plane and Solid Geometry for Colleges, Schools, and Private Students

Eli Todd Tappan - Geometry - 1873 - 288 pages
...sides (594). 773. Corollary — The radius being the same, two spherical triangles are equal, 1st. When they have two sides and the included angle of the one respectively equal to those parts of the other, and similarly arranged; 2d. When they have one side and the adjacent angles...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 562 pages
...let the triangle ACE = the triangle DFE. Bisect ECB with CH, and draw HE. The triangles HCB and HCE have two sides and the included angle of the one, respectively equal to the corresponding parts of the other, whence HE = HB. Now AH + HE > AE; but AH + HE = AH + HB = AB....
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...let the triangle ACE = the triangle DFE. Bisect ECB with CH, and draw HE. The triangles HCB and HCE have two sides and the included angle of the one, respectively equal to the corresponding parts of the other, whence HE = HB. Now AH + HE > AE; but AH + HE = AH + HB = AB....
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...it is greater than either of them. THEOREM X. 80. If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects. In the triangles ABC, DEF, let the side...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 454 pages
...indifferently. TWO SIDES AND INCLUDED ANGLE. 284. Theorem — Two triangles are equal when they have two sidex and the included angle of the one, respectively equal to two sides and the included angle of the other. If the angle A is equal to D, and the side AB to the side DF, and AC to DE, then the...
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