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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. "
Elements of Plane Geometry - Page 48
by Thomas Hunter - 1878 - 132 pages
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Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1889 - 80 pages
...is less. Proposition XXVI. A Theorem. 63. If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other, each to each, the other homologous parts are also equal, and the triangles are equal. Proposition XXVII. A Theorem....
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 442 pages
...BC = side YZ, side CA = side ZX ; and, finally, area ABC = area XYZ. Proposition 4. THEOREM — 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, then the triangles are identically...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry - 1891 - 422 pages
...equal to the given lines, and it is, therefore, the required triangle. PROPOSITION I. Theorem : // two triangles have two sides and the included angle...and the included angle of the other, each to each, they are equal in all their parts. Statement : Let the two triangles 123 and 456 have the side / 2...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry - 1891 - 428 pages
...coincide, and are equal. Conclusion \ABCK and E FS H being, etc. Corollary I. Parallelograms having two sides and the included angle of the one equal to two...and the included angle of the other, each to each, are equal. PROPOSITION XVIII. 21O. Theorem : A parallelogram is divided by either of its diameters...
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The Colliery Engineer Pocket-book of Principles Rules, FormulŠ, and Tables ...

Thomas J. Foster - Coal mines and mining - 1891 - 456 pages
...opposite or vertical angles are equal. 4. If two angles have their sides parallel they are equal. 5. If two triangles have two sides and the included angle...the one, equal to two sides and the included angle of the other, they are equal in all their parts. If two triangles have two angles and the included...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry - 1891 - 426 pages
...equal to the given lines, and it is, therefore, the required triangle. PROPOSITION I. 122. Theorem : // two triangles have two sides and the included angle of the one equal to two sides and the included anyle of the other, each to each, they are equal in all their parts. Statement : Let the two triangles...
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The Elements of Physics

Henry Smith Carhart, Horatio Nelson Chute - Physics - 1892 - 400 pages
...triangles .4KB and A'KB, we have the angles at A' equal, and hence right angles, and AK= A'K, since the triangles have two sides, and the included angle of the one equal to the corresponding parts of the other. dicular to MN, and A' is as far back of MN as A is in front....
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Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 524 pages
...C. PROPOSITION XLII. THKOREM. 127. Two parallelograms which have two tides and the included angle of one equal to two sides and the included angle of the other, each to each, are equal in aU respect*. I) Let AD and A' D' represent, two parallelograms in whicli AB equal* A'...
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Geometry for Grammar Schools

Ephraim Hunt - Geometry - 1894 - 118 pages
...ABC and DEF are equal in all respects. Because, (1) We have made two sides and the included angle of one equal to two sides and the included angle of the other, each to each. (2) Put the vertex D upon vertex A; side DE upon side AB, and as they are equal, the point E will fall...
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Mathematics for Common Schools: A Manual for Teachers, Including Definitions ...

John Henry Walsh - 1896 - 282 pages
...that two triangles are equal in every respect (a) when two sides and the included angle of one are equal to two sides and the included angle of the other, each to each ; and (6) when two angles and the included side of one are equal to two angles and the included side of the...
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