 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...to trihedral or polyhedral angles that correspond to the following theorems of plane geometry : (a) The sum of two sides of a triangle is greater than the third side. (6) If two angles of a triangle are equal, the opposite sides are equal. (c) If two sides of a triangle... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...equidistant from three given lines. UNEQUAL LINES AND UNEQUAL ANGLES PROPOSITION XXVIII. THEOREM 127. The sum of two sides of a triangle is greater than the third side. B Given A A To prove AB + AC> BC. HINT. See Axioms. Ex. 302. Is it possible to draw a triangle whose... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...equidistant from three given lines. UNEQUAL LINES AND UNEQUAL ANGLES , PROPOSITION XXVIII. THEOREM 127. The sum of two sides of a triangle is greater than the third side. Given A A CB. B A To prove AB + AC>So. HINT. See Axioms. Ex. 302. Is it possible to draw a triangle... | |
 | American Mathematical Society - Mathematics - 1913 - 876 pages
...the primary merit of being always true. Take the theorem which scandalized the sophists of old : " The sum of two sides of a triangle is greater than the third side." We take an isosceles triangle ABC, where AB = AC; A, remaining always on the perpendicular bisector... | |
 | Michael Angelo McGinnis - Equations, Theory of - 1913 - 47 pages
...sum of the squares of two numbers or quantities is greater than the greater number.) (9) a + /3 > 7. (The sum of two sides of a triangle is greater than the third side.) (See any geometry for proof.) (10) Assume that 7-/3=A£. Then A/3+ ^8 = 7. Let A/3 = x. Then, x + J3... | |
 | Mathematics - 1915 - 830 pages
...above. There are certain properties of a triangle which are equally true in P and 'on S. For example, the sum of two sides of a triangle is greater than the third side, and their difference is less than the third side. That not all the relations are the same is apparent... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 282 pages
...congruent to A LMR A UK is congruent to A LMR BOOK I. PLANE GEOMETRY PROPOSITION XXIV. THEOREM 86. The sum of two sides of a triangle is greater than the sum of two lines drawn to the extremities of the third side, from any point within the triangle. Given:... | |
 | Ernst Rudolph Breslich - Mathematics - 1916 - 392 pages
...the straight line-segment joining the points (§3). The following theorems express inequalities : 12. The sum of two sides of a triangle is greater than the third side, and their arithmetical difference is less than the third side. The first part of this theorem follows... | |
 | Mathematics - 1917 - 284 pages
...extremities of EF form with EF the triangle desired. The proof of this is left to the student. 74. Theorem: The sum of two sides of a triangle is greater than the third side. 3 Given: In the triangle CAB let AB be the longest side. To Prove: AC + CB > AB. Proof: AC + CB > AB... | |
 | Herbert Ellsworth Slaught - 1918 - 344 pages
...of the circumscribed polygons will continually decrease. This is easily seen by using the fact that the sum of two sides of a triangle is greater than the third side. INSCRIBING A SQUARE IN A CIRCLE 462. PROBLEM. To inscribe a square in a circle. n Construction. Through... | |
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The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side. 
