 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 in all their parts." Axiom 1. "Things which are equal to the same thing, are equal...  Elements of Geometry and Trigonometry - Page 16by Adrien Marie Legendre - 1838 - 269 pagesFull view - About this book
 | Edward Olney - Geometry - 1883 - 344 pages
...will fall in AD or AD produced, as E'H'. Now, the two triangles AE'B and DH'C are equal, since they have two sides and the included angle of the one equal to two sides and the included angle of the other; viz., AB = DC, being opposite sides of a parallelogram; and fora like reason BE' = CH'.... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...required triangle. For, all triangles constructed with the given data must be equal, since they would have two sides and the included angle of the one equal to two sides and the included angle of the other. \ QEF PROBLEM XI. One side of a triangle and its adjacent angles being given, to construct... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...falls between CA and CB, and CH will meet AB in some point, as H. Draw HE. The triangles HCB and HCE have two sides and the included angle of the one, equal to the corresponding parts of the other, whence HE = HB (?). Now AH + HE > AE but AH + HE = AH + HB =... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...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 - Geometry - 1884 - 242 pages
...+ 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 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... | |
 | 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?... | |
 | 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... | |
 | 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... | |
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