 | S.S. Kutateladze - Mathematics - 2005 - 442 pages
...triangle. Then this arc divides this triangle into two triangles ACD and BCD. In both these triangles, the sum of any two sides is greater than the third side. Indeed, (I) CD < AD + AC by assumption; (2) if, say, AC = AD + CD, AD + CD is a shortest arc emanating... | |
 | Haym Kruglak, John Moore, Ramon Mata-Toledo - Mathematics - 1998 - 508 pages
...The sum of the angles in a triangle is 180°, or is equal to two right angles. 2. In every triangle the sum of any two sides is greater than the third side; the difference of any two sides is less than the third side. 3. The angles opposite equal sides are... | |
 | Clayton W. Dodge - Mathematics - 2004 - 310 pages
...greater angle. 19. 1n a triangle the greater angle lies opposite the greater side. 20. ln a triangle the sum of any two sides is greater than the third side. 22. To construct a triangle from three given segments. 23. To construct at a point on a line an angle... | |
 | Jeff Kolby - Education - 2021 - 612 pages
...the sides containing the right angle) = -AB-AC = 2 -10-102 50 The answer is (B). 61. In a triangle, the sum of any two sides is greater than the third side. Hence, x + y > z. We are given y/x = 3. Multiplying both sides of this equation by x yields y = 3x.... | |
 | Jeff Kolby - Reference - 2021 - 590 pages
...(B) 4x<z (C) 4jcsz (D) 4x = z ' (E) It cannot be determined from the information given In a triangle, the sum of any two sides is greater than the third side. Hence, x + y > z. We are given y/x = 3. Multiplying both sides of this equation by x yields y = 3x.... | |
 | S.S. Kutateladze - Mathematics - 2005 - 442 pages
...triangle. Then this arc divides this triangle into two triangles ACD and BCD. In both these triangles, the sum of any two sides is greater than the third side. Indeed, (1) CD < AD+AC by assumption; (2) if, say, AC = AD+CD, AD + CD is a shortest arc emanating... | |
 | Brainard Braimah - Mathematics - 2007 - 254 pages
...A, B, C Angles: a, ft, % Sides: a, b, c Triangle inequality: Triangle inequality: In any triangle, the sum of any two sides is greater than the third side and this statement is called the triangle inequality. For example, AC + CB > AB Triangular numbers: Numbers... | |
 | V Krishnamurthy, C R Pranesachar - Mathematics - 2007 - 708 pages
...CA. If AC and BD meet at O, prove that AOBA is congruent to A0CD. 1 1. Deduce from theorem 10, that the sum of any two sides is greater than the third side in any triangle. 12. In AABC, AB>AC. LetD on AB be such that AD = AC. Then prove that ZADC = (ZB +... | |
 | Euclid - Euclid's Elements - 1920 - 304 pages
...similar to that of the enunciation of Prop. 17: see the note on that proposition. The meaning is that the sum of any two sides is greater than the third side. According to Proclus, it was the habit of the Epicureans to ridicule this theorem as being evident... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 356 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. 
