| Webster Wells - 1908 - 174 sider
...Subtracting AC from both members of the inequality, AB>BC-AC. ~ V •-A\^ PROP. -XL THEOREM <&&: Tlie **sum of any two sides of a triangle is greater than the** su-ttvof the lines drawn from any point within the triangle to the extremities of the remaining side.... | |
| Trinity College (Dublin, Ireland) - 1910
...proportional between, two lines whose lengths are 2 and 3 cms. or halfinches. Theoretical. 4. Prove that **the sum of any two sides of a triangle is greater than the third side.** 5. Show how to construct a triangle equal in area to a polygon having five or more sides. 6. Prove... | |
| David Eugene Smith - 1910 - 287 sider
...also r ? From these relations find the number of degrees in p + q + r. /* PROPOSITION 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... | |
| George William Myers - 1910 - 282 sider
...1-4 will now be shown to be immediate 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;... | |
| Clara Avis Hart, Daniel D. Feldman - 1911 - 303 sider
...sum of any two angles of a triangle is less than two right angles. PROPOSITION XVIII. THEOREM 167. **The sum of any two sides of a triangle is greater than the third** sideGiven AJ.BC. To prove a -{. c>bAKGUMBNT 1. Prolong c through B until prolongation £D = a. 2. Draw... | |
| Clara Avis Hart, Daniel D. Feldman, John Henry Tanner, Virgil Snyder - 1912 - 188 sider
...last 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.... | |
| George Wentworth, George Albert Wentworth, David Eugene Smith - 1913 - 470 sider
...also r ? 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... | |
| John Charles Stone, James Franklin Millis - 1916 - 174 sider
...one 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 Charles Stone, James Franklin Millis - 1916 - 278 sider
...line-segment that 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,... | |
| John H. Williams - 1916 - 162 sider
...that line. 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... | |
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