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" If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. "
New Plane and Solid Geometry - Page 50
by Webster Wells - 1908 - 298 pages
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Elements of Geometry: With Notes

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...
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Elements of Geometry and Conic Sections

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...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

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...
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Elements of Geometry and Trigonometry: With Practical Applications

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...
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Elements of Geometry: With Practical Applications to Mensuration

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...
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

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...
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Elements of Geometry: With Practical Applications to Mensuration

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...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 444 pages
...triangles are equal (285), and AH is equal to CH, and BH to DH. 363. Theorem. — If the <fo'a^ronafe of a quadrilateral bisect each other, the figure is a parallelogram, To be demonstrated by the student. RECTANGLE 363. If one angle of a parallelogram is right, the others...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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, the figure is a, parallelogram. Let the diagonals of the quadrilateral ABCD bisect each other in E. Then, the triangles AED and CEB...
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Treatise on Plane and Solid Geometry for Colleges, Schools, and Private Students

Eli Todd Tappan - Geometry - 1873 - 288 pages
...equal. Therefore, the triangles are equal (285), and AH is equal to CH, and BH to DH. 362. Theorem — If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. To be demonstrated by the student. RECTANGLE 363. If one angle of a parallelogram is right, the others...
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