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" If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal. "
The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ... - Page 39
by Edward Brooks - 1868 - 275 pages
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 455 pages
...to be proved. PROPOSITION IX. THEOREM. If two spherical triangles on the same, or on equal spheres, have two angles and the included side of the one equal...the included side of the other, each to each, the remaining parts will be equal, each to each Let the spherical triangles ABC and EFG, have the angle...
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First Lessons in Geometry: In Two Parts

B. Marks - 1875
...a parallelogram, the interior alternate angles r and m are equal. Then the two triangles adb, bdc, have two angles and the included side of the one equal...and the included side of the other, each to each, and are therefore equal; And the side ab opposite the angle m is equal to the side cd opposite the...
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Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - Measurement - 1875 - 184 pages
...angle COR is equal to the angle COR', since each is a right angle. Hence, the two triangles COR and COR have two angles, and the included side of the one...and the included side of the other, each to each, and are therefore equal in all their parts. Hence, OR, opposite the angle OCR, is equal to OR'. opposite...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 366 pages
...GEOMETRY. PROPOSITION VIII. THEOREM. If two spherical triangles have two angles and the included side of one, equal to two angles and the included side of the other, each to each, their remaining parts are equal, each to each. Let FGH and ACD be two spherical triangles, in which...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1876 - 239 pages
...on equal spheres, two sphev'cal triangles having two angles and the included side of the one eqval to two angles and the included side of the other, each to each, areequal, or symmetrical and equivalent. DEM.—Using the same triangles as in the preceding proposition,...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 443 pages
...the included angle of the one equal to two sides and the included angle of the other each to each, or two angles and the included side of the one equal to two angles and the included side of the other. PROPOSITION XV. TIIEOREM. In an isosceles spherical triangle, the angles opposite the equal sides are...
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Elements of Plane Geometry, Part 1

Thomas Hunter - 1878
...sides. If perpendiculars be let fall from any point, two right-angled triangles will be formed having two angles and the included side of the one equal...and the included side of the other, each to each. 5. The circle ABD is described upon the radius AB of the circle AEC: it is required to prove that the...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 266 pages
...&ABC= &DEF ABG=DEF Proposition 8. Theorem.—If two triangles have two angles and the included side of one, equal to two angles and the included side of...each, the triangles will be equal in all their parts. DEF, DFE, and the side EF. The triangles will be equal in all their parts. Apply the triangle ABC to...
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A Treatise on Special Or Elementary Geometry: Including an Elementary, and ...

Edward Olney - Geometry - 1879 - 440 pages
...angle E, and that the areas are equaL Fio. 204. PROPOSITION VH. 286. Theorem. — Two triangles which have two angles and the included side of the one equal to two angles and tlie included side of the other, each to each, are equal. ^ Pro. 805. DEM.— Let ABC and DEF be two...
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