 | Elias Loomis - Conic sections - 1877 - 458 pages
...is equal to 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,... | |
 | Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...be equal. the angles CBE and FAD are equal (Prop. XXXIII., Bk. I.). Hence these triangles have two sides and the included angle of the one equal to two...and the included angle of the -other, each to each; they are, thereF ED CJPJ! C AB A. B fore, equal in all their parts. If, now, from the whole figure... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...Angle DBA = 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 - 1882 - 262 pages
...spherical triangle are equal the triangle is equilateral. PROPOSITION XVI. 581. Theorem. — On the same or on equal spheres two isosceles triangles having two sides and the included angle of the one equal te two sides and the included angle of the other, each to each, can be superimposed, and are consequently... | |
 | 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... | |
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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... 
