| 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... | |
| 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... | |
| William Chauvenet, William Elwood Byerly - 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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'B°I the triangles /^B /^' BC = B'C' j" are congruand zB = /iB' J ent. Proof.—... | |
| John Macnie - Geometry - 1895 - 390 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... | |
| George Albert Wentworth - Mathematics - 1896 - 68 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... | |
| 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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