 | William Guy Peck - Conic sections - 1876 - 412 pages
...draw the arc DA'. The right• angled triangles AED and A 'ED, have two sides and the included atigle of the one, equal to 'two sides and the included angle of the other, each to each ; hence, they are equal in all their parts ; therefore, the angle EA'D is equal to EAD, and the side... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...CD, and BC is common to the two triangles ABC, BCD, the two triangles ABC, BCD have two sides and the included angle of the one equal to two sides' and the included angle of the other; therefore the side AC is equal to BD (Pr. 6), and the angle ACB to the angle CBD. And,... | |
 | 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... | |
 | Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...the angle EDC is equal to the angle FDC (Def. 10.). Hence the 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, and are equal in all their parts (Prop. IV.). Therefore CE is equal to CF. The angle CED is an acute... | |
 | 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 the... | |
 | 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 is... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...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
...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... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...TW. 6. Comparing with (4), TU> TV. QED 45 THEOREM XIX. 108. If two triangles .have two sides and the included angle of 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
...TRIANGLES. PROPOSITION IV. 298. Theorem. — Two triangles which have two sides and the included angle of one equal to two sides and the included angle of the other, each to each, are equal. DEMONSTRATION. Let ABC and DEF be two triangles, having AC = DF, AB = DE, and angle A =... | |
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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... 
