 | John Radford Young - Euclid's Elements - 1827 - 228 pages
...diagonals of a rhomboid, therefore, bisect each other. PROPOSITION xxxi. THEOREM. (Converse of Prop. XXX.) If the diagonals of a quadrilateral bisect each other, the figure is a rhomboid. If the diagonals AC, BD (preceding diagram), bisect each other, ABCD is a rhomboid. For the... | |
 | Elias Loomis - Conic sections - 1860 - 246 pages
...will be a rectangle. Prop- 9. The parallelogram whose diagonals are equal is rectangular. Prop. 8. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. Prop. 10. Any line drawn through the centre of the diagonal of a parallelogram to meet the sides, is... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...Therefore the diagonals of a rhombus bisect each other at right angles. PROPOSITION XXXV. — THEOREM. 115. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. Let ABCD be a quadrilateral, and DC AC, DB its diagonals intersecting at E ; then will the figure be a... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...Therefore the diagonals of a rhombus bisect each other at right angles. PROPOSITION XXXV. — THEOREM. 115. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. Let ABCD be a quadrilateral, and D AC, DB its diagonals intersecting at E ; then will the figure be a parallelogram.... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...Therefore the diagonals of a rhombus bisect each other at right angles. PROPOSITION XXXV. — THEOREM. 115. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. Let ABCD be a quadrilateral, and DC AC, DB its diagonals intersecting at E ; then will the figure be a... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...equal. Therefore, the triangles are equal (285), and AH is equal to CH, and BH to DH. 363. Theorem — If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. To he demonstrated by the student. RECTANGLE 363. If one angle of a parallelogram is right, the others... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...Therefore the diagonals of a rhombus bisect each other at right angles. PROPOSITION XXXV. — THEOREM. 115. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. Let ABCD be a quadrilateral, and AC, DB its diagonals intersecting at E ; then will the figure be a parallelogram.... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...vertex to the middle of the base bisects the vertical angle (87). PROPOSITION XXXIV.— THEOREM. 112. If the diagonals of a quadrilateral bisect each other,...diagonals of the quadrilateral ABCD bisect each other in E. Then, the triangles AED and CEB are equal (76), and the angles EAD, ECB, respectively opposite... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...vertex to the middle of the base bisects the vertical angle (87). PROPOSITION XXXIV.— THEOREM. 112. If the diagonals of a quadrilateral bisect each other,...diagonals of the quadrilateral ABCD bisect each other in E. Then, the triangles AED and CEB are equal (76), and the angles EAD, ECB, respectively opposite... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...necessarily a parallelogram? 85. The diagonals of a parallelogram bisect each other. 86. (Converse of 85.) If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. 881 (Converse of 87.) If the diagonals of a quadrilateral bisect each other at right angles, the figure... | |
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If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. 
