 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.  Solid Geometry - Page 434by John Charles Stone, James Franklin Millis - 1916 - 174 pagesFull view - About this book
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...dihedrah will be equal each to each; and the trihedrals will be congruent or symmetrical (V., 34). xxii. If two spherical triangles on the same sphere, or equal spheres, have tivo sides and th& included angle of the one equal to two sides and- the included angle of the other,... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...equal in either case in all its parts to DEF. Proposition 10. Theorem.—If two triangles, on the same or equal spheres, have two sides and the included angle of one respectively equal to the two sides and the included of another, they are equal in all their parts.... | |
 | 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 - 1894 - 172 pages
...mutually equilateral, their polar tnangles are mutually equiangular. • PROPOSITION XVII. THEOREM. 629. If two spherical triangles on the same sphere, or...equal respectively to two sides and the included angle of the other, I. They are equal if the equal parts occur in the same order. II. They are symmetrical... | |
 | Webster Wells - Geometry - 1894 - 394 pages
...mutually equiangular. (The proof is left to the student ; compare § 627.) PROPOSITION XVII. THEOREM. 629. If two spherical triangles on the same sphere, or...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... | |
 | Webster Wells - Geometry - 1894 - 398 pages
...mutually equiangular. PROPOSITION XVII. THEOREM. 629. If two spherical triangles on the same sphere, Br equal spheres, have two sides and the included angle...equal respectively to two sides and the included angle of the other, I. They are equal if the equal parts occur in the same order. II. They are symmetrical... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...Z»,F, and ZJ = Z 7). Whence, J.5(7 and D^J? ' are equal. (§ 629, I.) PROPOSITION XVIII. THEOREM. 630. If two spherical triangles on the same sphere, or equal spheres, have a side and two adjacent angles of one equal respectively to a side and two adjacent angles of the other,... | |
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