 | Henry William Watson - Geometry - 1871 - 320 pages
...lines may be of constant length. MISCELLANEOUS EXAMPLES ON BOOK I. 1. Prove that the angle between the bisectors of two consecutive angles of a quadrilateral is equal to half the sum of its other two angles. 2. Prove that the sum of the distances of any point taken within... | |
 | George Minchin Minchin - 1877 - 470 pages
...-7-5 — — j from the centre. 12. Every body has one and only one centre of gravity. Hence show that the lines joining the middle points of the opposite sides of a quadrilateral bisect each other. (Consider four equal particles at the vertices). 13. From the vertices of a given triangle let perpendiculars... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...Two quadrilaterals whose diagonals are respectively equal and form equal angles are equivalent. 157. Lines joining the middle points of the opposite sides of a quadrilateral bisect each other. 158. If lines are drawn from the vertices of a square bisecting the opposite sides in order, there... | |
 | George Minchin Minchin - Statics - 1880 - 536 pages
...distance «t from the centre. -R'-r2 1 2. Every body has one and only one centre of mass. Hence show that the lines joining the middle points of the opposite sides of a quadrilateral bisect each other. (Consider four equal particles at the vertices.) 13. From the vertices of a given triangle let perpendiculars... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...Two quadrilaterals whose diagonals are respectively equal and form equal angles are equivalent. 157. Lines joining the middle points of the opposite sides of a quadrilateral bisect each other. 158. If lines are drawn from the vertices of a square bisecting the opposite sides in order, there... | |
 | Charles Scott Venable - 1881 - 380 pages
...parallelogram, to prove the parallelogram one-fourth of the quadrilateral, using (24). 54. The lines which join the middle points of the opposite sides of a quadrilateral, bisect each other. (Corollary of 53. ) 55. If, through the extremities of each diagonal of a quadrilateral, parallels... | |
 | Samuel Constable - Geometry - 1882 - 222 pages
...parallelogram ; and its area is half that of the quadrilateral. [Consider Prop. 1.] 3. The straight lines joining the middle points of the opposite sides of a quadrilateral bisect each other. [This follows immediately from the last, if it can be shewn that the diagonals of a parallelogram bisect... | |
 | George Minchin Minchin - Physics - 1884 - 372 pages
...distance cr3 -= ; from the centre. 12. Every body has one and only one centre of mass. Hence show that the lines joining the middle points of the opposite sides of a quadrilateral bisect each other. (Consider four equal particles at the vertices.) 13. From the vertices of a given triangle let perpendiculars... | |
 | Simon Newcomb - Geometry, Analytic - 1884 - 462 pages
...middle points of the opposite sides, and thus show that the three points are coincident. 10. Prove that the lines joining the middle points of the opposite sides of a quadrilateral and the line joining the middle points of the diagonals all bisect each other. To do this, express... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...H are the middle points of AD, CD, BC, and AB respectively, prove that EFGH is a parallelogram. 8. The lines joining the middle points of the opposite sides of a quadrilateral bisect the line joining the middle points of the diagonals. 9. If D and E are the middle points of the sides... | |
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The lines joining the middle points of the opposite sides of a quadrilateral bisect each other. 
