 | George Clinton Shutts - Geometry - 1912 - 392 pages
...diagonal of a convex spherical polygon is as great as 180° of arc. PROPOSITION XXIX. 750. THEOREM. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. Z-B+ZO 180° and LA + LB the polar of B = 180°— I', C = 540° Given A ABC. To Prove ZA ZC < 540°.... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Solid - 1912 - 220 pages
...75°, 85°, and 145°. Find the sides of its polar triangle. 434 l> PROPOSITION XIII. THEOREM 435 949. The sum of the angles of a spherical triangle is greater than 180° and less than 340°. Given spherical A ABC with sides denoted by a, b, and c. To prove ZA + Zn + ZC> 180° and <... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...Ax. 9 Ax. 9 §654 and Similarly B + b' = 180°, and C + c' = 180°. PROPOSITION XIII. THEOREM 668. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. Given a spherical triangle ABC, the letter at the vertex of each angle denoting its value in degrees,... | |
 | George C. Shutts - 1913 - 212 pages
...triangle are equal, the triangle is isosceles. 454 SOLID CiEOMETRY PROPOSITION XXIX. 752. THEOREM. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. Given A ABC. To Prove ZA+Z#+ZC> 180° and Z A + Z B + Z C < 540°. Proof. Sue. 1. Let A A'B'C' be the... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 pages
...respectively, find the sides of the polar triangle (in degrees). Why? Why? (c) § 361 367. Theorem IX. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. FIG. 249 Given the spherical A ABC with the sides a, b, and c. To prove that ZA + ZB+ZO 180° and <... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...180°, and Z (7+ c' = 180°. The proof of (6) is left for the student. EXERCISE 302 303 367. Theorem IX. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. FIG. 249 Given the spherical A ABC with the sides a, b, and c. To prove that ZA + ZB+ZO 180° and <... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...producing the sides of A ABC, all the other relations are proved. QED PROPOSITION XIII. THEOREM 668. The sum of the angles of a spherical triangle is greater than 180° and Zes.s than 540°. Given a spherical triangle ABC, the letter at the vertex of each angle denoting its... | |
 | Education - 1913 - 396 pages
...plane parallel to the base is a figure of the same shape as the base (Prove for circular cone only) 7 The sum of the angles of a spherical triangle is greater than 180° but less than 540° 8 The planes which bisect the dihedral angles of a trihedral angle intersect in... | |
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The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC... 
