| Edward Atkins - 1877 - 68 pages
...a given point within, then the line bisecting the third angle will pass through the same point. 22. **The difference of any two sides of a triangle is less than the third side.** 23. If the angles at the base of a right-angled isosceles triangle be bisected, the bisecting lins... | |
| James Maurice Wilson - 1878 - 448 pages
...But AD is equal to AB and BC together, therefore AB and BC are together greater than AC\. QED COR. **The difference of any two sides of a triangle is less than the third side.** THEOREM 13. If from the ends of the side of a triangle two straight lines be drawn to a point within... | |
| Edward Harri Mathews - 1879 - 90 pages
...sides of a triangle are together greater than the third side. Hence prove that the difference between **any two sides of a triangle is less than the third side.** Section II. 1. If a side of any triangle be produced, the exterior angle is equal to the two interior... | |
| Mary W I. Shilleto - 1882 - 414 pages
...angles to the given line. 2. Any two sides of a triangle are together greater than the third side. **The difference of any two sides of a triangle is less than the third side.** 3. If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle... | |
| Samuel Constable - Geometry - 1882 - 218 pages
...I. 21.] 3. Prove, by showing that the angle BDC is greater than the angle BCD in fig. Prop. 13, that **the difference of any two sides of a triangle is less than the third.** 4. Prove that the angle included between any two straight lines is equal to the angle included between... | |
| Marianne Nops - 1882 - 274 pages
...as a fraction of a right angle the interior angle of a regular octagon. 13. The difference between **any two sides of a triangle is less than the third side.** 14. Describe an equilateral triangle having its side equal to a given finite straight line, and having... | |
| Mathematical association - 1883 - 86 pages
...opposite to it. THEOR. 13. Any two sides of a triangle are together greater than the third side. COR. **The difference of any two sides of a triangle is less than the third side.** THEOR. 14. If from the ends of a side of a triangle two straight lines are drawn to a point within... | |
| Euclides - 1884 - 434 pages
...any two sides ; .-. the sum of any two sides of a triangle is greater than the third side. COR. — **The difference of any two sides of a triangle is less than the third side.** For BA + AC is greater than BC. I. 20 Taking AC from each of these unequals, there remains BA greater... | |
| Mathematical association - 1884 - 146 pages
...Similarly it may be shown that AC and CB are together greater than AB, and CB and BA than AC. QED COR. **The difference of any two sides of a triangle is less than the third side.** D 2 *Ex. 1 8. The straight line drawn from the vertex of a triangle to the middle point of the base... | |
| Science - 1884 - 534 pages
...PQ. Let QD cut А В in E, and join EP : with this construction the proof is obvious. PROP. 20. 54. **The difference of any two sides of a triangle is less than the third side.** 55. A point P is taken within the triangle А В С ; show that the cum of the distances PA, PB, and... | |
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