 | Benjamin Greenleaf - 1869 - 516 pages
...by construction, AG is equal to DE ; hence AH is equal to D F. Therefore the two triangles AGH, DEF, having two sides and the included angle of the one...and the included angle of the other, each to each, are themselves equal (Prop. V. Bk. I.). But the triangle AGH is similar to ABC ; therefore DEF is also... | |
 | Bernhard Marks - Geometry - 1869 - 172 pages
...ADC. Therefore the angle AB c is equal to the angle ADC. Then the two triangles AB c, AD c, have two sides, and the included angle of the one equal to...and the included angle of the other, each \ to each, and are equal in all their parts ; that is, the three angles of the one are equal to the three angles... | |
 | Bernard Marks - Geometry - 1871 - 172 pages
...the areas of the triangles ? d bcef DEMONSTRATION. We wish to prove, that, If two triangles have two sides, and the included angle of the one equal to...and the included angle of the other, each to each, the two triangles are equal in all respects. Let the triangles abc and d ef have the side ab of the... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...is equal to CD, and BC is common to the two triangles <VBC BCD, the two triangles ABC, BCD have two sides and the included angle of the one, equal to two sides and the in. duiled angle of the other ; therefore, the side AC is equa\ to BD (Prop. VI.), and the angle ACB... | |
 | Edward Olney - 1872 - 270 pages
...their parts, and can be applied so as to coincide. PROPOSITION XV. 301, TheoTem.—Two parallelograms having two sides and the included angle of the one...and the included angle of the other, each to each, are equal. DEM.—Let AC and EG be two parallelograms, with AD — EH, AB = EF, and A = E; then are... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...equilateral. PROPOSITION XTI. 581. Theorem, — On the same 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. DEM.— In the triangles ABC and AB'C', let AB = AC,... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...join A' and C" by the arc of a great circle : then, because the triangles BA C and B'A'C' have two sides and the included angle of the one, equal to...and the included angle of the other, each to each, the remaining parts will be equal, cod' to each; that is, A'Q' — AC, and the angle A' equal to the... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 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 (40). • 49i Schotium. In equal triangles the equal angles are opposite the... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...CDB ; therefore the whole angle ABC = A DC ; therefore the triangles ABC and ADC, having two sidi-s and the included angle of the one equal to two sides and the included angle of the other, are equal (40). 49. Scholium. In equal triangles the equal angles are opposite the equal... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...equilateral. PROPOSITION XVL SSI, Theorem, — On the same or on equal spheres two isosceles triangles having two sides and the included angle of the one equal to tioo sides and the included angle of the other, each to each, can be superimposed, and are consequently... | |
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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... 
