 | William Guy Peck - Conic sections - 1876 - 376 pages
...C'. Lay off EA' equal to EA, and draw the arc DA'. The rightangled triangles AED and A'ED, have two sides and the included angle 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... | |
 | Edward Olney - Geometry - 1877 - 272 pages
...form of quadrilateral.] PROPOSITION XV. 301, Theorem,—Two parallelograms having two sides and tin Included angle of the one equal to two sides and the included angle of the other, each to each, are equal. DEM.—Let AC and EC be two parallelograms, with AD = EH, AB... | |
 | 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 sides 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,... | |
 | 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).... | |
 | 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... | |
 | 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
...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... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...hence, « -j- I = b + c ; but a + b hence EAB = CAD. Hence the triangles 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, each to each. .-. (1) ABE = AD C. H Again, the triangle ABE and the square AK have the... | |
 | 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' =... | |
 | 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... | |
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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... 
