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" The lines joining the mid-points of the opposite sides of a quadrilateral bisect each other. "
New Plane and Solid Geometry - Page 65
by Wooster Woodruff Beman, David Eugene Smith - 1899 - 382 pages
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...concave, convex, and cross quadrilaterals, and for the special case of an interior angle of 180°.) 168. The lines joining the mid-points of the opposite sides...other. Consider for the special cases mentioned in ex. 167. 169. The line joining the mid-points of the diagonals of a quadrilateral, and the lines joining...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...concave, convex, and cross quadrilaterals, and for the special case of an interior angle of 180°.) 168. The lines joining the mid-points of the opposite sides...other. Consider for the special cases mentioned in ex. 167. 169. The line joining the mid-points of the diagonals of a quadrilateral, and the lines joining...
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New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...here easily proved by prop. XXVII, cor. 2 ; for if a = b, then a! = 6'; but p II e, .-. p ± a', .-. x = b = a.) a' b' 113. The lines joining the mid-points...of its opposite sides, pass through the same point. EXERCISES. 119. What is the sum of the interior angles of a polygon of 20 sides ? of 30 sides ? 120....
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New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 265 pages
...proved by prop. XXVII, cor. 2 ; for if a = then of — b' • but p II e, .'. p J_ a', .'. cc = 6 = a.) a/ b' 113. The lines joining the mid-points of...of its opposite sides, pass through the same point. EXERCISES. 119. What is the sum of the interior angles of a polygon of 20 sides ? of 30 sides ? 120....
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...quadrilateral and the midpoints of the diagonals determine the vertices of a parallelogram. * Ex. 278. The lines joining the midpoints of the opposite sides of a quadrilateral and the line joining the midpoints of the diagonals meet in a point. (Exs. 277, 274.) Ex. 279. The...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...quadrilateral and the midpoints of the diagonals determine the vertices of a parallelogram. * Ex. 278. The lines joining the midpoints of the opposite sides of a quadrilateral and the line joining the midpoints of the diagonals meet in a point. (Exs. 277, 274.) Ex. 279. The...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...quadrilateral and the midpoints of the diagonals determine the vertices of a parallelogram. * Ex. 278. The lines joining the midpoints of the opposite sides of a quadrilateral and the line joining the midpoints of the diagonals meet in a point. (Exs. 277, 274.) Ex. 279. The...
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Plane Geometry

Arthur Schultze - 1901 - 260 pages
...quadrilateral and the midpoints of the diagonals determine the vertices of a parallelogram. * Ex. 278. The lines joining the midpoints of the opposite sides of a quadrilateral and the line joining the midpoints of the diagonals meet in a point. (Exs. 277, 274.) Ex. 279. The...
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Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...the same plane), show that the lines joining the midpoints of the sides form a parallelogram. Ex. 19. The lines joining the midpoints of the opposite sides of a quadrilateral in space bisect each other. Ex. 20. The planes bisecting the dihedral angles of a trihedral angle meet...
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Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...the same plane), show that the lines joining the midpoints of the sides form a parallelogram. Ex. 19. The lines joining the midpoints of the opposite sides of a quadrilateral in space bisect each other. Ex. 20. The planes bisecting the dihedral angles of a trihedral angle meet...
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