 | National Committee on Mathematical Requirements - Mathematics - 1922 - 84 pages
...corresponding parts of the other; (c) they are mutually equilateral; (d) they are mutually equiangular. 45. The sum of any two face angles of a trihedral angle is greater than the third face angle. 46. The sum of the face angles of any convex polyhedral angle is less than four right angles.... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Solid - 1922 - 216 pages
...simply until a little later, in connection with our study of the sphere. Theorem 30 570. The sum of two face angles of a trihedral angle is greater than the third. O Given any trihedral angle O-XYZ. To prove that /.ZOY+Z. XOZ > Z_ XO Y. Proof. There is no necessity... | |
 | College Entrance Examination Board - Universities and colleges - 1922 - 124 pages
...100°. If the radius of the sphere is 14 inches, find the area of the triangle. 4. Prove that the sum of two face angles of a trihedral angle is greater than the third face angle. 5. Prove: If each of three intersecting planes is perpendicular to each of the other two... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...general, two symmetric polyhedral angles cannot be made to coincide. PROPOSITION XXIII. THEOREM 548. The sum of any two face angles of a trihedral angle is greater than the third face angle. Given ZA VC, the greatest face angle of trihedral angle v-ABC. To prove ZA VB + ZB VC>... | |
 | National Committee on Mathematical Requirements - Mathematics - 1923 - 680 pages
...corresponding parts of the other; (c) they are mutually equilateral; (d) they are mutually equiangular. 45. The sum of any two face angles of a trihedral angle is greater than the third face angle. 46. The sum of the face angles of any convex polyhedral angle is less than four right angles.... | |
 | Walter Burton Ford, Charles Ammermann - Geometry, Modern - 1923 - 406 pages
...Explain. 5. 7, § 236. 6. Why? 7. Why? 8. Why? 9. 1, §236. 10. § 53. 269. Theorem VI. The sum of two face angles of a trihedral angle is greater than the third. Given the trihedral angle V-ABC. To prove that Z AVB + /. BVC > /.AVC. Proof. If ZA VC is equal to... | |
 | David Eugene Smith - Geometry, Solid - 1924 - 256 pages
...consider only convex spherical polygons. 132 BOOK VIII Proposition 8. Two Face Angles 194. Theorem. The sum of any two face angles of a trihedral angle is greater than the third face angle. Given the trihedral ZV-XYZ with face Z XVZ > face Z XVY or face Z YVZ. Prove that Z.XVY+... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1925 - 504 pages
...parts being arranged in the same order. [Proof by superposition.] PROPOSITION- XXVII. THEOREM 557. The sum of any two face angles of a trihedral angle is greater than the third face angle. Given ZAFC, the greatest face angle of trihedral angle V-ABC. To prove Z AVB + Z BVC >... | |
 | Baltimore (Md.). Department of Education - Mathematics - 1924 - 182 pages
...respectively, to the three face angles of another, the trihedral angles are either congruent or symmetric. 5 . The sum of any two face angles of a trihedral angle is greater than the third face angle. 6. The sum of the face angles of any convex polyhedral angle is less than four right angles.... | |
 | National Committee on Mathematical Requirements - Mathematics - 1927 - 208 pages
...the other; (c) they are mutually equilateral; (d) they are mutually equiangular. [80, 81, 82, 83] 45. The sum of any two face angles of a trihedral angle is greater than the third face angle. [33] 46. The sum of the face angles of any convex polyhedral angle is less than four right... | |
| |
The sum of any two face angles of a trihedral angle is greater than the third face angle. 
