 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...34). xxii. If two spherical triangles on the same sphere, or equal spheres, have tivo sides and th& included angle of the one equal to two sides and- the included angle of the other, each to each, the two triangles will be congruent or symmetrical, and hence equal (15). xxui. If two spherical triangles... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...required triangle. Proposition 7. Theorem.—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 triangles will be equal in all their parts. Let ABC, DEF be two triangles which have BA, AC, and... | |
 | Elias Loomis - Conic sections - 1880 - 452 pages
...therefore, A and B are mutually equilateral. PROPOSITION XII. THEOREM. If two triangles on equal spheres have two sides and the included angle of the one equal to two sides and the included anrjle of the other each to each, their third sides will be equal, and their other angles will be equal... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...angle DBC—CDB; therefore the whole angle ABC = ADC; therefore the triangles ABC and ADC, having two sides and the included angle of the one equal to two sides and the included angle of the other, are equal (80). 89. Scholium. In equal triangles the equal angles are opposite the equal... | |
 | 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
...diagonal PS. Then — 1. Because of the equations supposed in the hypothesis, the triangles PQS and ABC have two sides and the included angle of the one equal to two sides and the included angle of he other. Therefore the triangles are identically equal, and Area ABC = area PQS. (§ 108) 2. In... | |
 | 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 =... | |
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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 in all their parts." Axiom 1. "Things which are equal to the same thing, are equal... 
