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Books Books 51 - 60 of 122 on If two triangles have two sides, and the included angle of the one equal to two sides....
" 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 equal in all their parts. "
Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ... - Page 281
by Charles Davies - 1872 - 592 pages
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 366 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'...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 366 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...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1877 - 239 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...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 443 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,...
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Elements of Plane Geometry, Part 1

Thomas Hunter - 1878
...AF and FE are also equal (const.), and the angles AFC and EFB are equal (Prop. XVII.). Therefore the two triangles have two sides and the included angle...and the included angle of the other, each to each, and are every way equal (Prop. IV.); the angle EBF is equal to the angle FCA. But DBG is greater than...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1880 - 443 pages
...therefore, A 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...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 240 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...
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 399 pages
...Or, because QU= QW (I.), TQ+QU= TU> TW. 6. Comparing with (4), TU> TV. QED 45 THEOREM XIX. 108. If two triangles .have two sides and the included angle...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...
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 333 pages
...PROPOSITION XXI. 704. Theorem.—On the same sphere, or on equal spheres, two spherical triangles having two sides and the included angle of the one equal to two...and the included angle of the other, each to each, are equal, or symmetrical and equivalent. DEMONSTRATION. Let ABC and A'B'C' be two spherical triangles,...
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 267 pages
...required triangle. For, all triangles constructed with the given data must be equal, since they would have two sides and the included angle of the one equal to two sides and the included angle of the other. \ QEF PROBLEM XI. One side of a triangle and its adjacent angles being given, to construct...
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