| T S. Taylor - 1880 - 152 pages
...lines to cut off a part equal to the less. 3. 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 bases shall be equal. NOTE. — When two sides of a triangle have been mentioned, the third side... | |
| Simon Newcomb - Geometry - 1881 - 418 pages
...9) Or, because QU= QW (I.), TQ+QU= TU> TW. 6. Comparing with (4), TU> TV. QED 45 THEOREM XIX. 108. **If two triangles .have two sides and the included...the one equal to two sides and the included angle** of the other, they are identically equal. Hypothesis. ABC&n&MNP, two triangles in which PM = CA. PN... | |
| Edward Olney - Geometry - 1883 - 352 pages
...PROPOSITION XXI. 704. Theorem.—On the same sphere, or on equal spheres, two spherical triangles 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, or symmetrical and equivalent. DEMONSTRATION. Let ABC and A'B'C' be two spherical triangles,... | |
| 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... | |
| Edwin Abbott Abbott - Domestic education - 1883 - 236 pages
...triangles do you see that look equal ? " (Ans. ABE, ACD.) "Then we shall try to prove that these two **have two sides and the included angle of the one, equal to two sides** of the included angle of the other." This done, you say, " Now what other triangles look equal?" (Ans.... | |
| 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...and 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... | |
| |