 | Edward Olney - Geometry - 1872 - 472 pages
...inscribed in semicircles (211), and DB is a diameter. Therefore, AC = DB. QED 248. COR.— Conversely, If the diagonals of a parallelogram are equal, the figure is a rectangle. DEM.— Since the diagonals of a parallelogram bisect each other, if they are equal, a circumference... | |
 | Edward Olney - Geometry - 1877 - 272 pages
...angles, they are inscribed in semicircles (211), and DB is a diameter. Therefore, AC = DB. QED FIG. 185. 248. CoR.—Conversely, If the diagonals of a...semicircles, and consequently will be right angles. OF POLYGONS OF MORE THAN FOUR SIDES. 249. A Salient Angle of a polygon is one whose sides, when produced,... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...Hence AC and DB, being diameters of the same circle, are equal. QBD 255. COBOLLABY. — Conversely, // the diagonals of a parallelogram are equal, the figure is a rectangle. By (251) the parallelogram is circumscriptible ; whence, by (192) the angles are right angles. OF POLYGONS... | |
 | George Albert Wentworth - 1884 - 264 pages
...lines are parallel, and draw through one of the middle points a line parallel to the diagonal. 46. If the diagonals of a parallelogram are equal, the figure is a rectangle. 47. If the diagonals of a parallelogram are perpendicular to each other, the figure is either a rhombus... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...is a rhombus. 3. If the diagonals of a quadrilateral bisect its angles, the figure is a rhombus. 4. If the diagonals of a parallelogram are equal, the figure is a rectangle. PROPOSITION XL. THEOREM. 123. Two parallelograms are equal when two adjacent sides and the included... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 332 pages
...the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. 4. Theorem. — If the diagonals of a parallelogram are equal, the figure is a rectangle. ELEMENTS OF GEOMETRY. ARRANGEMENT OF WRITTEN EXERCISES. 64. In writing out a demonstration, brevity... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. 4. Theorem. — If the diagonals of a parallelogram are equal, the figure is a rectangle. ARRANGEMENT OF WRITTEN EXERCISES. 64. In writing out a demonstration, brevity of statement and clearness... | |
 | William Chauvenet - Geometry - 1887 - 364 pages
...the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. 4. Theorem.—If the diagonals of a parallelogram are equal, the figure is a rectangle. ARRANGEMENT OF WRITTEN EXERCISES. 64. In writing out a demonstration, brevity of statement and clearness... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...other, the figure is a parallelogram. . T» Ex.26. The diagonals of a rectangle are equal. Ex. 27. If the diagonals of a parallelogram are equal, the figure is a rectangle. Ex. 28. The diagonals of a rhombus are perpendicular to each other, and bisect the angles of the rhombus.... | |
 | George Albert Wentworth - 1889 - 276 pages
...lines are parallel, and draw through one of the middle points a line parallel to the diagonal. 46. If the diagonals of a parallelogram are equal, the figure is a rectangle. 47. If the diagonals of a parallelogram are perpendicular to each other, the figure is either a rhombus... | |
| |
If the diagonals of a parallelogram are equal, the figure is a rectangle. 
