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" VIf 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... "
Elements of Geometry and Conic Sections - Page 27
by Elias Loomis - 1849 - 226 pages
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Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - Measurement - 1875 - 284 pages
...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 equal to two angles 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...
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First Lessons in Geometry: In Two Parts

B. Marks - 1875 - 176 pages
...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 to two angles 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...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 412 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,...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...AGE (Pr. 5) ; and, by construction, BG is equal to GA ; hence the triangles BGF, AGE have two angles and the included side of the one equal to two angles...included side of "the other ; they are, therefore, equal (Pr. 7) ; and the angle BFG is equal to the angle AEG. But AEG is, by construction, a right angle,...
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Elements of Plane Geometry, Part 1

Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...same reason the angle BAE is equal to the angle CDE: the two triangles have, therefore, two angles and the included side of the one equal to two angles and the included side of the other, each to each; hence they are equal in all their parts (Prop. V., Bk. I.) ; the side AE is equal to...
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A Treatise on Special Or Elementary Geometry: Including an Elementary, and ...

Edward Olney - Geometry - 1879 - 502 pages
...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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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 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 the other, each to each, the triangles will be equal in all their parts. DEF, DFE, and the side EF. The triangles...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1880 - 456 pages
...of the one equal to two sides and the included angle of the other each to each, or two angles a-id the included side of the one equal to two angles and the included side of the other. PROPOSITION XV. THEOREM. In an isosceles spherical triangle, the angles opposite the equal sides are...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1880 - 452 pages
...etc. PROPOSITION XIII. THEOREM. If two triangles on equal spheres have two angles and the zncluded side of the one equal to two angles and the included side of the other each to each, their third angles will be equal, and their other sides will be equal each to each. If...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1882 - 262 pages
...areas are equal. Fio. 204. PROPOSITION vn. 286. Theorem.—Two triangles which have two angles and tie included side of the one equal to two angles and the included side of the other, each to each, are equal. FIG. 205. DBM.— Let ABC and DEF be two triangles, having angle A = angle...
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