 | William John M'Clelland - 1885 - 182 pages
...three given ares (any two of which being supposed greater than the third}. (Cf. Euc. I. xxii.) (7). If two triangles have two sides and the included angle...the included angle of the other, each to each, the triangles are equal in every respect. For, since two sides of given length intersecting at a given... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...CAG equal to the angle D (Post. 7) ; make AG equal to DE, and draw GC. Then the triangles AGC and DEF have two sides and the included angle of the one equal...and the included angle of the other, each to each ; consequently, GC is equal to EF (PV). Now, the point G may be without the triangle ABC, it may be... | |
 | Charles Davies - Geometry - 1886 - 352 pages
...(Ax. 3). In the same manner we may prove that the angle AED is equal to the angle CEB. THEOREM IV. If two triangles have two sides and the included angle...other, each to each, the two triangles will be equal. Let the triangles ABC and DEF have the side AC equal to DF, CB to FE, and the angle C equal to the... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...Proposition XLV. A Theorem. 87. Two parallelograms are equal if they have two sides and the included angle of one equal to two sides and the included angle of the other, each to each. Proposition XLVI. A Theorem. 88. Parallel lines are everywhere equally distant. VIII. POLYGONS OF MORE... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...Proposition XLV. A Theorem. 87. Two parallelograms are equal if they have two sides and the included angle of one equal to two sides and the included angle of the other, each to each. Proposition XLVI. A Theorem. VIII. POLYGONS OF MORE THAN FOUR SIDES. 89. What is a polygon ? a. A pentagon?... | |
 | Euclid - Geometry - 1890 - 442 pages
...= side XY, side 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... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 428 pages
...respectively equal to the given lines, and it is, therefore, the required triangle. PROPOSITION I. 122. Theorem : If two triangles have two sides and the...and the included angle of the other, each to each, they are equal in all their parts. , Statement : Let the two triangles / 2 3 and 456 have the side... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...TRIANGLES. SYNOPSIS.* SECTION I.— EQUAL TRIANGLES. 1O.>. i. DEFINITIONS. 2. PROPOSITIONS. PROP. I. If 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. PROP. II. If two triangles have two angles and the included side... | |
 | Seth Thayer Stewart - Geometry, Modern - 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... | |
 | Thomas J. Foster - Coal mines and mining - 1891 - 444 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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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. 
