 | George Bruce Halsted - Geometry - 1885 - 389 pages
...symmetrical is henceforth devoted entirely to such. THEOREM V. 688. Two spherical triangles having two sides and the included angle of one equal respectively to two sides and the included angle of the other, are either congruent or symmetrical. (1) If the parts given equal are arranged in the... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...symmetrical is henceforth devoted entirely to such. THEOREM V. 688. Two spherical triangles having two sides and the included angle of one equal respectively to two sides and the included angle of the other, are either congruent or symmetrical. (1) If the parts given equal are arranged in the... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...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 respectively to two 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,... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 150 pages
...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 respectively to two sides and the included angle of the other, are either equal or equivalent. Proof. By superposing one Sph. A upon the other, or upon... | |
 | Webster Wells - Geometry - 1894 - 394 pages
...627.) PROPOSITION XVII. THEOREM. 629. If two spherical triangles on the same sphere, or equal spheres, have two sides and the included angle of one equal respectively to two sides and the included anjle of the other, I. They are equal if tlte equal parts occur in the same order. II. They are symmetrical... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...hypothesis that angle «> angle c. Therefore AB<BC. QED PROPOSITION XXII. THEOREM 79. 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. C' GIVEN — AB, AC, and a, of the triangle ABC respectively... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...hypothesis that angle «>angle c. Therefore AB<BC. QED PROPOSITION XXII. THEOREM 70. 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. C' GIVEN — AB, AC, and a, of the triangle ABC respectively... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...equal, the figure is a rectangle. 46. Prove by coincidence that two parallelograms are equal if they have two sides and the included angle of one equal respectively to two sides and the included angle of the other. 42 PLANE GEOMETRY PROPOSITION XXVIII 109. Theorem. // two sides of a quadrilateral are... | |
 | Henry W. Keigwin - Geometry - 1897 - 254 pages
...PROBLEM. To construct a square on a given side. PROPOSITION XXVI. THEOREM. 115. If two parallelograms have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the parallelograms are equal. 7 ».D *a FIG. 53. [Superpose, and use Ax. III.] 116. COR.... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...§ 600.) PROP. XXII. THEOREM. 602. If two spherical triangles on the same sphere, or equal spheres, have two sides and the included angle of one equal,...respectively, to two sides and the included angle of the other, II. They are symmetrical if the equal parts occur in the reverse order. I. Given ABC... | |
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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. 
