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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... "
Elementary Geometry: With Applications in Mensuration - Page 97
by Charles Davies - 1850 - 216 pages
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Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...34). xxii. If two spherical triangles on the same sphere, or equal spheres, have tivo sides and th& included angle of the one equal to two sides and- the included angle of the other, each to each, the two triangles will be congruent or symmetrical, and hence equal (15). xxui. If two spherical triangles...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...required triangle. Proposition 7. Theorem.—If two triangles have two sides and the included angle of one, equal to two sides and the included angle of the other, each to each, the triangles will be equal in all their parts. Let ABC, DEF be two triangles which have BA, AC, and...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 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 (80). 89. Scholium. In equal triangles the equal angles are opposite the equal...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1880 - 452 pages
...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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First principles of Euclid: an introduction to the study of the first book ...

T S. Taylor - 1880 - 152 pages
...lines to cut off a part equal to the less. 3. If two triangles have two sides and the included angle of one, equal to two sides and the included angle of the other each to each, the bases shall be equal. NOTE. — When two sides of a triangle have been mentioned, the third side...
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 418 pages
...= right angle DBC+ angle ABC. Angle FBC = right angle FBA + angle ABC. Therefore the two triangles having two sides and the included angle of the one equal to tAvo sides and the included angle of the other are identically equal, so that Area ABD = area FBC....
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 344 pages
...? PROPOSITION XIX. 701. Theorem.—On the same sphere, 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. DEMONSTKATION. In the triangles ABC and AB'C', let...
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 352 pages
...in AD or AD produced, as E'H'. Now, the two triangles AE'B and DH'C are equal, since they have two sides and the included angle of the one equal to two sides and the included angle of the other; viz., AB = DC, being opposite sides of a parallelogram ; and for a like reason BE' =...
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...< D. Hence, since A is neither > D nor < D, A must •— D. Then in the two triangles, we have two sides and the included angle of the one equal to two sides and the included angle of the other; hence, they are equal in all their parts; hence, B = E and C =: F. Therefore, etc. Scholium.—In...
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The Eclectic School Geometry: A Revision of Evan's School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...triangles be similar. Take AG equal to DE, and AH to DF; also, join GH. Then the triangles AGH, DEF, having two sides and the included angle of the one equal to two sides and the included angle of the other, are equal throughout (Theo. XII, Book I). Now, by hypothesis, Hence, it follows that...
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