 | Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...propositions. Great importance will be attached to accuracy.] 1. The sum of any two sides of a triangle is greater than the third side, and their difference is less than the third side. 2. If two quadrilaterals ABCD, EFGH have the four angles A, B, C, D respectively equal to the four... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...lines or medians of the triangle. PROPOSITION XVI. — THEOREM. The sum of any two sides of a triangle is greater than the third side, and their difference is less than the third side. Given. — Let ABC be a triangle. To Prove. — We are to prove that AC+ BC> AB, and also AB BC < AC.... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 246 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. 141. Two right triangles are equal if the hypotenuse and an acute angle of the one are equal, respectively,... | |
 | Thomas Ulvan Taylor, Charles Puryear - Trigonometry - 1902 - 268 pages
...geometry. In any spherical triangle 1. The greater side is opposite the greater angle, and conversely. 2. The sum of any two sides is greater than the third side. 115 SrHERICAL TRIGONOMETRY 3. The sum of the sides is less than 3Ü0°. 4. The sum of the angles is... | |
 | George Albert Wentworth - Geometry - 1904 - 496 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 In the triangle ABC, let AC be the longest side. To prove that AB + BC > AC, and AC - BC < AB. Proof.... | |
 | James Morford Taylor - Trigonometry - 1905 - 256 pages
...The sum of the sides is less than 360°, and the sum of the angles lies between 180° and 540°. IV. The sum of any two sides is greater than the third side. NOTE. The three following principles are often useful in determining the relation of an unknown part... | |
 | George William Myers - Mathematics - 1910 - 304 pages
...consequences of Axioms 8 and 10. PROPOSITION I 196. Theorem: The sum of any two sides of a triangle is greater than the third side, and their difference is less than the third side. Given any triangle ABC. To prove: a+b>c; b+c>a; a—b<.c; b—c<.a; b—a<.c; c— 6<a; Proof: Consider... | |
 | David Eugene Smith - Geometry - 1911 - 370 pages
...triangle. Then TP = TS. By measuring TB, BS can then be found. THEOREM. The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side. If the postulate is assumed that a straight line is the shortest path between two points, then the... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...AB<AC + BC. We infer from this that a triangle can be constructed with three given lines as sides, when the sum of any two sides is greater than the third side. 74. Construction I. To construct a triangle, given the three sides. c The method of construction is... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...AB<AC + BC. We infer from this that a triangle can be constructed with three given lines as sides, when the sum of any two sides is greater than the third side. 74. Construction I. To construct a triangle, given the three sides. The method of construction is shown... | |
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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. 
