 | Evan Wilhelm Evans - 1884 - 170 σελίδες
...similar. Take AG equal to DE, and AH to DF; also, join GH. Then the triangles AGH, DEF, having two sides and the included angle of the one equal to two sides and the included angle of the other, are equal throughout (Theo. XII, Book I). Now, by hypothesis, Hence, it follows that... | |
 | Evan Wilhelm Evans - 1884 - 242 σελίδες
...+ DB < AC + CB. NOTE. — Have pupils give demonstration, prolonging BD instead of AD. THEOREM XII. 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, they are equal throughout. The... | |
 | William John M'Clelland - 1885 - 182 σελίδες
...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 one equal to two sides and the included angle of the other, each to each, the triangles are equal in every respect. For, since two sides of given... | |
 | Charles Davies, Adrien Marie Legendre - 1885 - 538 σελίδες
...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 to two sides and the included angle of the other, each to each ; consequently, GC is equal to EF (PV). Now, the point G may be without... | |
 | Euclid - 1890 - 442 σελίδες
...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 - 1891 - 428 σελίδες
...TRIANGLES. SYNOPSIS.* SECTION I.— EQUAL TRIANGLES. 1O.>. i. DEFINITIONS. 2. PROPOSITIONS. PROP. I. If two triangles have two sides and the included angle...the one equal to two sides and the included angle of the other, each to each, they are equal in all their parts. PROP. II. If two triangles have two... | |
 | Thomas J. Foster - 1891 - 444 σελίδες
...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... | |
 | Seth Thayer Stewart - 1891 - 422 σελίδες
...equal to the given lines, and it is, therefore, the required triangle. PROPOSITION I. Theorem : // two triangles have two sides and the included angle...the one equal to two sides and the included angle of the other, each to each, they are equal in all their parts. Statement : Let the two triangles 123... | |
 | Seth Thayer Stewart - 1891 - 426 σελίδες
...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... | |
 | Seth Thayer Stewart - 1891 - 428 σελίδες
...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 sides and the included angle of the other, each to each, are equal. PROPOSITION XVIII. 21O. Theorem : A parallelogram is divided... | |
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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. 
