 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Solid - 1919 - 240 pages
...properties specified under (1). Let t3 be a trihedral angle symmetrical to tl. Then fcj = t3. § 142 .-. f1 and t2 are symmetrical. The proof of the second part...point B is taken so that DB = DE, and that AB and BC are drawn. Then prove (1) AB=AE, (2) AC<AB + BC, (3) EC < BC, (4) £EDC<£ BDC, (5) ^ ADC < £ ADB... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Solid - 1919 - 232 pages
...^ and £2 are symmetrical. The proof of the second part is left to the student. 151. THEOREM XXVIT. The sum of two face angles of a trihedral angle is...Proof : Connect points A and C on two sides. Suppose £ADO/.ADB, Construct DE making Z ADE = Z ADB. Suppose that point B is taken so that DB = DE, and that... | |
 | Herbert Ellsworth Slaught - Geometry, Solid - 1919 - 244 pages
...student. 151. THEOREM XXVII. The sum of two face of a trihedral angle is greater than the third face Outline of Proof : Connect points A and C on two sides. Suppose ^ ADC>/. ADB. Construct DM making Z ADE = Z ADB. Suppose that point B is taken so that DB = DE, and... | |
 | United States. Office of Education - 1921 - 1286 pages
...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. 4(1. The sum of the face angles of any convex polyhedral angle is less than four right angles. 47.... | |
 | Education - 1921 - 1190 pages
...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. 4fi. The sum of the face angles of any convex polyhedral angle is less than four right angles. 47.... | |
 | College Entrance Examination Board - Universities and colleges - 1922 - 124 pages
...90°, and 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 planes, the... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Solid - 1922 - 216 pages
...be proved 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... | |
 | National Committee on Mathematical Requirements - Mathematics - 1922 - 84 pages
...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. 47. Each... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...angles are right angles. (d) The sum of the face angles of a polyhedral angle is less than 360°. (e) The sum of two face angles of a trihedral angle is greater than the third face angle. (/) If the opposite face angles of a tetrahedral angle are equal, the opposite dihedral angles are... | |
 | Walter Burton Ford, Charles Ammermann - Geometry, Modern - 1923 - 406 pages
...3. Why? 4. 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... | |
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The sum of any two face angles of a trihedral angle is greater than the third face angle. 
