 | Edward Olney - Geometry - 1882 - 262 pages
...plane triangles. PROPOSITION XI. 569. Theorem. — The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than Ihe third side. DEM.— Let ABC be any spherical triang'e; then is BC < BA + AC, and BC — AC < BA... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...plane triangles. PROPOSITION XIV. 689. Theorem. — The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side. DEMONSTRATION. Let ABC be any spherical triangle. Then is BC < BA + AC, and BC- AC < BA; and the same... | |
 | H. C. Godwin - Railroad engineering - 1890 - 396 pages
...(5) The greater angle is always opposite the greater side. No angle or side is greater than 180°. The sum of any two sides is greater than the third side. The sum of the three sides is less than 360°. Given a, b, and C, to find A and B ; use Eqs. 2a and... | |
 | George Bruce Halsted - Geometry - 1896 - 208 pages
...less than the third side. AB - BC < AC; .: AB < AC+BC. Therefore : 227. Theorem. In every triangle the sum of any two sides is greater than the third side. CHAPTER X. POLYGONS. 228. A number of sects, the second beginning at the end point of the first, the... | |
 | George Albert Wentworth - Geometry - 1895 - 468 pages
...figures, are called homologous. 137. THEOREM . The sum, of two sides of a triangle is greater tf'ian the third side, and their difference is less than the third side. PROPOSITION XXIII. THEOREM. 138. The sum, of the three angles of a triangle is equal to two right angles.... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...a straight line is the perpendicular bisector of that line. 137. The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side. 138. The sum of the three angles of a triangle is equal to two right angles. 139. Cor. 1. If the sum... | |
 | George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...therefore greater than either of them. PROPOSITION XIX. THEOREM. 138. Tlie sum of two sides of a triangle is greater than the third side, and their difference is less than the third side. •a. O In the triangle ABC, let AC be the longest side. To prove that AB + BC> AC, and AC — BC <... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...therefore greater than either of them. PROPOSITION XIX. THEOREM. 138. The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side. B AO In the triangle ABC, let AC be the longest side. To prove that AB + BC> AC, and AC - BC < AB.... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...called the median, or medial line. 17 Proposition 7. Theorem. 17. The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side. To prove the first part, consult Ax. 20. The second part can be obtained from the first part by the... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...sides and the homologous angles of equal triangles are equal. 138. The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side. 139. Two triangles are equal if two angles and the included side of the one are equal, respectively,... | |
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The sum of any two sides is greater than the third side, and their difference is less than the third side. 
