| 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... | |
| William Frothingham Bradbury - Geometry - 1880 - 260 pages
...and the 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... | |
| Elias Loomis - Conic sections - 1880 - 452 pages
...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... | |
| 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
...= right angle DBC+ angle ABC. Angle FBC = right angle FBA + angle ABC. Therefore the two triangles **having two sides and the included angle of the one equal to** tAvo sides and the included angle of the other are identically equal, so that Area ABD = area FBC.... | |
| Edward Olney - Geometry - 1883 - 344 pages
...? PROPOSITION XIX. 701. Theorem.—On the same sphere, or on equal spheres, two isosceles triangles **having two sides and the included angle of the one...and the included angle of the other, each to each,** can be superimposed, and are consequently equal. DEMONSTKATION. In the triangles ABC and AB'C', let... | |
| Edward Olney - Geometry - 1883 - 352 pages
...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 for a like reason BE' =... | |
| Alfred Hix Welsh - Geometry - 1883 - 326 pages
...< D. Hence, since A is neither > D nor < D, A must •— D. Then in the two triangles, we have two **sides and the included angle of the one equal to two sides and the included angle** of the other; hence, they are equal in all their parts; hence, B = E and C =: F. Therefore, etc. Scholium.—In... | |
| Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...triangles be 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... | |
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