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" If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal. "
The Elements of Geometry - Seite 266
von George Bruce Halsted - 1886 - 366 Seiten
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 426 Seiten
...PROPOSITION XLIV. THEOREM. 140. Two parallelograms, having two sides and the included angle of the one equal respectively to two sides and the included angle of the other, are equal in all respects. B СВ' С' A -------- DA, In the parallelograms AB С D and A' B' С' D', let...
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Elements of Geometry

George Albert Wentworth - 1881 - 266 Seiten
...PROPOSITION XLIV. THEOREM. 140. Two parallelograms, having two sides and the included angle of the one equal respectively to two sides and the included angle of the other, are equal in all respects. B CD О A DA' 111 the parallelograms AB С D and A' B' C' D', let AB = A'B',...
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The Elements of Geometry

George Bruce Halsted - 1885 - 389 Seiten
...have central symmetry in a plane, either can be made to coincide with the other by turning it in trie plane through a straight angle. This holds good when...given equal are arranged in the same order, as in DEF and ABC, then the triangle DEF can be moved in the sphere until it coincides with ABC. THEOREM...
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The Elements of Geometry

Webster Wells - 1886 - 392 Seiten
...and D'DC are equal, and their planes are parallel (§ 455). Then the parallelograms AB' and DC' have two sides and the included angle of one equal respectively to two sides and the included angle of the other. Therefore the faces AB' and DC' are equal (§ 123), and their planes are parallel. In...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - 1890 - 418 Seiten
...to one of its sides. Proposition 9. Theorem.* 709. Two triangles on the same, or on equal spheres, having two sides and the included angle of one equal...sides and the included angle of the other, are either equal or equivalent. Hyp. Let ABC, DEF be two A s having the side AB = DE, the side AC = DF, and the...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - 1890 - 420 Seiten
...reduced to one of its Proposition 9. Theorem.* 7O9. Two triangles on the same, or on equal spheres, having two sides and the included angle of one equal respectively to iwo sides and the included angle of the other, are either equal or equivalent. Hyp. Let ABC, DEF be...
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Introductory Modern Geometry of Point, Ray, and Circle

William Benjamin Smith - 1892 - 160 Seiten
...two triangles congruent ? 47. Theorem XIII. — Two A having two sides and the included angle of the one equal respectively to two sides and the included angle of the other are congruent. The data are: Two A, ABC and A'B'C, having the three equalities, AB = A'B', AC = A'C', a...
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Introductory Modern Geometry of Point, Ray, and Circle

William Benjamin Smith - 1892 - 314 Seiten
...two triangles congruent? 47. Theorem XIII. — Two A having two sides and the included angle of the one equal respectively to two sides and the included angle of the other are congruent. The data are: Two A, ABC and A'£'C', having the three equalities, A£ = A'£'9 AC = A'C',...
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The Elements of Solid Geometry: With Numerous Exercises

Arthur Latham Baker - 1893 - 150 Seiten
...other line joining the two points. QED PROPOSITION IX. THEOREM. 275. Two triangles on equal spheres, having two sides and the included angle of one equal...sides and the included angle of the other, are either equal or equivalent. Proof. By superposing one Sph. A upon the other, or upon its symmetrical, the...
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Introductory Modern Geometry of Point, Ray, and Circle

William Benjamin Smith - 1893 - 330 Seiten
...two triangles congruent? 47. Theorem XIII. — Two A having two sides and the included angle of the one equal respectively to two sides and the included angle of the other are congruent. The data are : Two A, ABC and A'B'C, having the three equalities, AB = A'B', AC = A'C',...
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