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" If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other... "
Elements of Geometry: With, Practical Applications - Page 28
by George Roberts Perkins - 1850 - 320 pages
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...GEOMETRY. EQUALITY OF TRIANGLES. THEOREM XXIV. 83. Two triangles are equal in all their parts if tivo sides and the included angle of the one are respectively equal to two sides and the included angle of the other. In the As ABC and DEF, let AB =DE, AC = DF, and Z. a = Z. b . А в DE To prove that...
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...GEOMETRY. EQUALITY OF TRIANGLES. THEOREM XXIV. 83. Two triangles are equal in all their parts if two rides and the included angle of the one are respectively equal to two sides and the included angle of the other. In the As ABC and DEF, let AB =J)E, AC — DF, and Z. a = Z. b . ABDE To prove that A...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 331 pages
...other. Suggestion. Prove EOH = FOH. PROPOSITION VI.—THEOREM. 20. Two triangles are equal when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. In the triangles ABO, DEF, let AB be equal to DE, BCto EF, and the included angle B equal...
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Elementary Synthetic Geometry of the Point, Line and Circle in the Plane

Nathan Fellowes Dupuis - Geometry - 1889 - 370 pages
...TRIANGLES. 52. Theorem. — Two triangles are congruent when two sides and the included angle in the one are respectively equal to two sides and the included angle in the other. IfAB = A'B'l the triangles BC = B'C'fare congruand L&=L&' } ent. Proof.— Place AABC...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1892 - 468 pages
...Two triangles on the same sphere, or equal spheres, are equal or equivalent, if two sides and tfie included angle of the one are respectively equal to two sides and the included angle of the otlier. I. In the triangles ABC and DEF let angle A equal angle D, and the sides AB and AC equal...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...other, the opposite (or vertical) angles are equal. PROPOSITION VI. Two triangles are equal when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. PROPOSITION VII. Two triangles are equal when a side and the two adjacent angles of the...
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Elementary Synthetic Geometry of the Point, Line and Circle in the Plane

Nathan Fellowes Dupuis - Geometry - 1894 - 313 pages
...TRIANGLES. 52. Theorem. — Two triangles are congruent when two sides and the included angle in the one are respectively equal to two sides and the included angle in the other. If AB=-A'BI the triangles /^B /^' BC = B'C' j" are congruand zB = /iB' J ent. Proof.—...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 392 pages
...vertices they pass is equilateral. PROPOSITION XXXIX. THEOREM. 143. Two parallelograms are equal if two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. A' Given: In parallelograms AC and A'C', AB equal to A'B', AD equal to A'D', and angle...
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Syllabus of Geometry

George Albert Wentworth - Geometry - 1896 - 50 pages
...equivalent. 749. Two triangles on the same sphere, or equal spheres, are equal or equivalent, if two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. 750. Two triangles on the same sphere, or equal spheres, are equal or equivalent, if...
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Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...PROPOSITION XII. THEOREM. 600. Two spherical triangles on the same sphere are equal or equivalent when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. I. Given— ABC and DEF two spherical triangles, on the same sphere, having AB = DE,...
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