| Andrew Bell - 1837 - 240 páginas
...one of its sides. 9. To bisect a parallelogram by a line drawn from a point in one of its sides. 10. **A line joining the middle points of two sides of a triangle, is parallel to the** base, and equal to the half of it. 11. The quadrilateral formed by joining the successiYe middle points... | |
| 1847
...middle points of the edges AC, AB, BD, BC, DA, DC respectively. Then, since the line drawn to bisect **two sides of a triangle is parallel to the third side, and equal to** half of it, we have BC = 2KN = 2HG, DC = 2MG = 2LK, AC = 2HL = 2MN, DA = 2KH = 2GN, AB = 2LG = 2KM,... | |
| George Salmon - 1852 - 316 páginas
...triangle meet on the internal bisector of the third angle : interpreted the other way, express that the **line joining the middle points of two sides of a triangle is parallel to the third side.** 5. We give now some examples of the use of these equations of the first degree. Ex. 1. Tiie bisectors... | |
| Euclides - 1853
...equal to four right angles. 10. To describe a square equal to the difference of two given squares. II. **A line joining the middle points of two sides of a triangle is parallel to the** "base, and equal to half of it. 12. To bisect a given parallelogram by a line drawn from a point in... | |
| 1856
...is an easy deduction, from any one of this series, that a straight line cutting off' equimultiples **of two sides of a triangle is parallel to the third side ; and,** conversely, a parallel to one side cuts off equimultiples of the other two sides. We need now to have... | |
| Euclides - 1858
...The square of a line is equal to four times the square of its half. 11. The st. line which bisects **two sides of a triangle, is parallel to the third side, and equal to one-half of** it. 12. If two sides of a triangle be given, its area will be greatest when they contain a rt. angle.... | |
| Euclides - 1860
...the given point, and such, that the line joining them shall be parallel to the other given line. 49. **A line joining the middle points of two sides of a triangle, is parallel to the** base, and equal to the half of it. • I 50. The quadrilateral formed by joining the successive middle... | |
| Euclides - 1860
...equidistant from P, and the line BC joining them is parallel to AE. EXERCISE XLIX. — THEOREM. The **line joining the middle points of two sides of a triangle is parallel to the** base, and equal to the half of it. Let ABC be a triangle, the line DE, that joins the middle points... | |
| James L. McDowell - 1867 - 102 páginas
...same point and cut each other in a point of trisection. (EXERCISES, p. 3, No. 5.) Also the straight **line joining the middle points of two sides of a triangle is parallel to the third side, and equal to** half of it. (1) Let AB CD be a rhombus. In the triangles ABC, ADC, the sides AB, AC are equal to AD,... | |
| Euclides - 1870
...square of a st. line is equal to four times the square of its half. 11. The st. line which bisects **two sides of a triangle, is parallel to the third side, and equal to** one half of it. 12. If two sides of a triangle be given, its area will be greatest when they contain... | |
| |