 | Clara Avis Hart, Daniel D. Feldman - Geometry, Solid - 1912 - 220 pages
...step in the argument he should state which of these suppositions have been proved false. 167. The sum of any two sides of a triangle is greater than the third side. 168. Any side of a triangle is less than the sum and greater than the difference of the other two.... | |
 | Queensland. Department of Public Instruction - Education - 1912 - 234 pages
...of the other. Find under what circumstances the triangles must be congruent. 2. Prove that the sum of any two sides of a triangle is greater than the third side. A, B, C, D, E are any five points in a plane. Prove that AB + AC + AD + AE is greater than one quarter... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...From these relations find the number of degrees in p + q + r. /* PEOPOSITION XX. THEOREM 112. The sum of any two sides of a triangle is greater than the third side, and the difference between any two sides is less than the third side. AB Given the triangle ABC, with... | |
 | Michael Angelo McGinnis - Equations, Theory of - 1913 - 47 pages
...(The nth root of the sum of two numbers is greater than the greater number.) But 7 < a + /3. (The sum of any two sides of a triangle is greater than the third side.) (7) Assume that 7 - /3 = A/3. Then, A/3 + /3 = 7. Let a = A/3. Then, (8) x + /3 = y. We now have the... | |
 | John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...equal to an angle of the other, and the including sides proportional, they are similar. § 146. The sum of any two sides of a triangle is greater than the third side. § 148. If two triangles have two sides of one equal respectively to two sides of the other, but the... | |
 | John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...92. If one of two parallel lines is perpendicular to a third line, the other is also. 107. The sum of any two sides of a triangle is greater than the third side. 109. The sum of the angles of a triangle is equal to two right angles. 114. In an equiangular triangle... | |
 | John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...can be drawn from the point to the line. The proof is left to the student. 146. Theorem. — The sum of any two sides of a triangle is greater than the third side. Hypothesis. A ABC is any triangle. Conclusion. AC + BC > AB. Suggestions. Produce AC through C to D,... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Plane - 1917 - 330 pages
...are the sides adjacent to the right angle. 78. Property of a triangle immediately inferred. The sum of any two sides of a triangle is greater than the third aide. For a straight line is the shortest line joining two points. (§ 9.) Ex. 1. Point out the hypothesis... | |
 | David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...that ZA> Z5. Accordingly, we conclude that the theorem is true. 88 Exercises. Inequalities 1. The sum of any two sides of a triangle is greater than the third side, and the difference between any two sides is less than the third side. Use Post. 3 for the first statement... | |
 | Cambridge Philosophical Society - Mathematics - 1927 - 1078 pages
...opposite to the greater angle), and from i. 18 its converse i. 19, from which he deduces i. 20 (the sum of any two sides of a triangle is greater than the third side). Now propositions i. 18, 19 and 20 are true for triangles of all magnitudes in the Elliptic Plane, although... | |
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The sum of any two sides of a triangle, is greater than the third side. 
