 | 1865 - 128 pages
...B + ft cos3 B + 7 cos C sin2 B) (aa + i0 + C7). 3. To find the equation to the circle described on the line joining the middle points of two sides of a triangle. Let D, F (Fig. 3) be the middle points of BC, BA; join DF and draw the perpendiculars DH, FK. Then... | |
 | Mathematics - 1865 - 132 pages
...B + ft cos3 B + y cos C sin2 B) (aa + bft + cy). 3. To find the equation to the circle described on the line joining the middle points of two sides of a triangle. Let D, F (Fig. 3) be the middle points of BC, BA ; join DF and draw the perpendiculars DH, FK. Then... | |
 | James McDowell - Mechanics - 1867 - 120 pages
...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 - 270 pages
...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... | |
 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...Therefore DQ=D R. Consequently PR, which is equal to P D+DR, is equal to P D+D Q. Therefore EC=P D+D Q. 2. The line joining the middle points of two sides of a triangle is equal to half the third side, and is parallel to it. Let ABC be the triangle, D and E the middle points... | |
 | Euclides - 1874 - 120 pages
...BC in 0. Join PO and draw AQ- parallel to it. Then PQ shall bisect the triangle.] 53. 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. 54. The straight lines joining the middle points of the four sides of any quadrilateral... | |
 | John Reynell Morell - 1875 - 220 pages
...corresponding height are given. EXERCISES ON BOOK III. 92. The straight line which joins the centres of two sides of a triangle is parallel to the third side, and equal to half that side. 93. The straight lines which join the centres of the consecutive sides of a quadrilateral... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...parallelogram (82) ; AE = EC; hence, DE bisects AC. GEOMETRY.— BOOK I. 104. Corollaries. 1. Tlie straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to its half. (?) 2. The straight line drawn from the middle point of one of the non-parallel sides of... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...triangle parallel to the base passes through the middle point of the other side. COR. 2. The straight line joining the middle points of two sides of a triangle is parallel to the base. [Cor. i. and Rule of Identity.] SECTION 4. PROBLEMS. PROB. i. To bisect a given angle. PROB.... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...of AB andD C shall divide the quadrilateral into two equal parts. 8. The straight line, which joins the middle points of two sides of a triangle, is parallel to the base. 9. If a straight line be divided into any two parts, the square on the whole line is equal to... | |
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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. 
