| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...construction, AG is equal to DE ; hence AH is equal to D F. Therefore the two triangles AGH, DE F1, having two sides and the included angle of the one equal to two...and the included angle of the other, each to each, are themselves equal (Theo. IV. Bk. I.) But the triangle AGH is similar to ABC; therefore DEF is also... | |
| William Frothingham Bradbury - Geometry - 1873 - 132 pages
...angle DBC = C DB ; 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). 49. Scholium. In equal triangles the equal angles are opposite the equal... | |
| Adrien Marie Legendre - Geometry - 1874 - 500 pages
...CB must be the prolongation of AC ; which was to be proved. PROPOSITION Y. THEOREM. If two triangles have two sides and the included angle of the one equal...and the included angle of the other, each to each, the triangles will be equal in att their parts. In the triangles ABC and DEF, let AB be equal to DE,... | |
| Benjamin Greenleaf - Geometry - 1874 - 206 pages
...construction, AG is equal to DE ; hence AH is equal to D F. Therefore the two triangles AGH, DE F. Laving two sides and the included angle of the one equal to two...and the included angle of the other, each to each, are themselves equal (Theo. IV. Bk. I.) But the triangle AGH is similar to ABC; therefore DEF is also... | |
| B. Marks - 1875 - 176 pages
...think of the areas of the triangles ? a d I cef DEMONSTRATION. We wish to prove, that, // two triangles have two sides, and the included angle of the one...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... | |
| William Guy Peck - Conic sections - 1876 - 376 pages
...meet at 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,...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 DA'... | |
| 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... | |
| 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 = EF, and A = E; then are they... | |
| Elias Loomis - Conic sections - 1877 - 458 pages
...because AB 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
...parallelograms 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...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... | |
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