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" Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other. 2. Two triangles are congruent if two angles and the included side of one are equal respectively to two angles... "
Solid Geometry, with Problems and Applications - Page 138
by Herbert Ellsworth Slaught, Nels Johann Lennes - 1911 - 190 pages
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...the second. THEOREM XII. 711. Two spherical triangles having two angles and the included side of the one equal respectively to two angles and the included side of the other, are either congruent or symmetrical. For the first triangle can be moved in the sphere into coincidence...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...the second THEOREM XII. 711. Two spherical triangles having two angles and the included side of the one equal respectively to two angles and the included side of the other, are either congruent or symmetrical. For the first triangle can be moved in the sphere into coincidence...
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Introductory Modern Geometry of Point, Ray, and Circle

William Benjamin Smith - Geometry, Modern - 1892 - 170 pages
...to pairs of equal parts. 48. Theorem XIV. — Two A having two angles and the included side of the one equal respectively to two angles and the included side of the other are congruent (Fig. 28). TA ~B\ I* B\ FIG. 28. Data: Two A ABC, A'B'C', having «=«', /?=/3', TH. XVI.] TRIANGLES....
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Introductory Modern Geometry of Point, Ray, and Circle

William Benjamin Smith - Geometry, Modern - 1892 - 314 pages
...to pairs of equal parts. 48. Theorem XIV. — Two A having two angles and the included side of the one equal respectively to two angles and the included side of the other are congruent (Fig. 28). FIG. 28. Data: Two A ABC, A'£'Cf, having «=«', (3 = f3', AB=A'B'. Proof. Fit ABQKA'B'-,...
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Introductory Modern Geometry of Point, Ray, and Circle

William Benjamin Smith - Geometry, Modern - 1893 - 330 pages
...lie opposite to pairs of 48. Theorem XIV. — Two A having two angles and the included side of the one equal respectively to two angles and the included side of the other are congruent (Fig. 28). FIG. 28. Data : Two AB=A'B'. A ABC, A'B'C', having «=«', /3 = /5', Proof. Fit AB on A'B'...
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Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 524 pages
...II ? Therefore PROPOSITION XXII. THBORBM. 547. Two triangles on the same sphere, or equal spheres, having two angles and the included side of one equal...two angles and the included side of the other, are equal or symmetrical. Suo. See figure and suggestions of Prop. XXL Therefore PROPOSITION XXIII. THEOREM....
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1894 - 412 pages
...Theorem. Two triangles on the same sphere, or equal spheres, having two angles and the included side 0f one equal, respectively, to two angles and the included side of the other, are either equal or symmetrical. Suggestion. See figure and suggestions for § 669. Therefore — Ex. 388....
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Elementary Solid Geometry and Mensuration

Henry Dallas Thompson - Geometry, Solid - 1896 - 226 pages
...either equal or symmetrical. 30. If two spherical triangles have two angles and the included side of the one equal respectively to two angles and the included side of the other, the two triangles are equal or symmetrical. 31. The angles at the base of an isosceles spherical triangle...
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The Elements of Geometry

Henry W. Keigwin - Geometry - 1897 - 254 pages
...[§ 37. Therefore, If two triangles have, etc. QED PROPOSITION II. THEOREM. 45. If two triangles have two angles and the included side of one equal respectively...to two angles and the included side of the other, the two triangles are equal. FlG. 23. Let ABC and DEF\>& two triangles in which angles B and C of the...
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Plane and Solid Geometry: Inductive Method

Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...write Prop. XVIII. 663. PROPOSITION XIX. Given: Two triangles on the. same sphere, or equal spheres, having two angles and the included side of one equal...to two angles and the included side of the other. (1) Can you prove the triangles equal? (2) Can you prove the triangles symmetrical ? Study the figures...
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