 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, I.  Solid Geometry - Page 396by John H. Williams, Kenneth P. Williams - 1916 - 162 pagesFull view - About this book
 | Sophia Foster Richardson - Geometry, Solid - 1914 - 236 pages
...placed in reverse order. (§ 393) 146 407. THEOREM. If two spherical triangles on the same sphere or on equal spheres have two sides and the included angle...equal respectively to two sides and the included angle of the other, they are congruent or symmetrical according as the parts given equal are placed in the... | |
 | Henry Parker Manning - Geometry - 1914 - 375 pages
...PNN' and M'Q'Q mutually equilateral, and ZM'Q'Q = Z.PNN'. Finally, now, the triangles PNQ and M'Q' N' have two sides and the included angle of one equal respectively to two sides and the included angle of the other, and ZM'N'Q' = Z.PQN. But the angle M'N'Q' is a right angle. Therefore PQN is a right... | |
 | Horace Wilmer Marsh - Mathematics - 1914 - 272 pages
...Finish the demonstration. Method of Indicating Equal Parts. The figures below represent triangles having two sides and the included angle of one, equal respectively to two sides and the included angle of the other. FIG. 1. The equal angles are shown by the same number, one being primed. The equal sides... | |
 | Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...be true ? Answer the same question for the conclusion. PROPOSITION I. THEOREM 63. 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 congruent. ABDE Hypothesis. In A ABC and A DEF: Conclusion. A ABC ^... | |
 | Mathematics - 1915 - 830 pages
...crayons, a pair of scissors, a bottle of glue and a ball of twine. Let them construct two triangles having two sides and the included angle of one equal respectively to two sides and the included angle of the other, cut these out, fit them together and see for themselves that they will coincide in all... | |
 | John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...outside of A ABC and Q falls outside of A DEF, and give the proof of the theorem. 479. Theorem. — If two spherical triangles on the same sphere or equal...equal respectively to two sides and the included angle of the other, they are either congruent or symmetrical. Hypothesis. A ABC and A DEF are spherical triangles... | |
 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 504 pages
...angles of the other, whether taken in the same or in opposite orders. PROPOSITION XXII. THEOREM 703. If two spherical triangles on the same sphere, or equal...equal respectively to two sides and the included angle of the other, I. They are congruent if the equal parts occur in the same order. II. They are symmetrical... | |
 | William Betz - Geometry - 1916 - 536 pages
...angles of the other, the triangles are congruent, (asa) Second Law of Congruence. 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 congruent, (sas) Third Law of Congruence. If two triangles have the... | |
 | William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...§ 815. 818. Two spherical triangles, on the same sphere or on equal spheres, are congruent if they have two sides and the included angle of one equal respectively to two sides and the included angle of the other and arranged in the same order, and symmetric if the given parts of one are arranged in... | |
 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...about all triangles made according to the directions ? PROPOSITION I. THEOREM 63. 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 congruent. ABDE Hypothesis. In A ABC and A DEF: AB = DE; AC=DF; ZJ.... | |
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