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" If two sides of a quadrilateral are equal and parallel, the figure is a parallelogram. "
Mathematics, mechanics, heat - Page 31
by American School (Chicago, Ill.) - 1903
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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

George Washington Hull - Geometry - 1807 - 408 pages
...parallel to BC. Therefore ABCD is a parallelogram by definition. § 74 QED PROPOSITION XXXI. THEOREM. 83. If two sides of a quadrilateral are equal and parallel, the figure is a parallelogram. Given — The quadrilateral ABCD, with AB equal and parallel to DC. To Prove — ABCD a parallelogram....
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...sides are parallel. Consequently the figure is a parallelogram (D. XXV.). THEOREM XXX. If two opposite sides of a quadrilateral are equal and parallel, the figure is a parallelogram. In the quadrilateral ABCD, suppose AB equal and parallel to DC, then will the figure be a parallelogram....
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 474 pages
...sides are parallel. Consequently the figure is a parallelogram (D. XXV.). THEOREM XXX. If two opposite sides of a quadrilateral are equal and parallel, the figure is a parallelogram. In the quadrilateral ABCD, suppose AB equal and parallel to DC, then will the figure be a parallelogram....
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The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - Geometry - 1868 - 284 pages
...AD is parallel to BC; therefore, the figure ABCD is a parallelogram. Therefore, etc. THEOREM XVII. If two sides of a quadrilateral are equal and parallel,...parallelogram. Let ABCD be a quadrilateral, having the sides AB and DC equal and parallel; then will ABCD be a parallelogram. For, draw the diagonal DB....
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...that is, the figure is a parallelogram (D. 28) ; which was to be proved. PROPOSITION XX*- THEOREM. If two sides of a quadrilateral are equal and parallel, the figure is a parallelogram. In the quadrilateral ABCD, let AB D be equal and parallel to DC: then will / \^ the figure be a parallelogram....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...are parallel. Therefore ABCD is a parallelogram. PROPOSITION XXXII.— THEOREM. 108. If two opposite sides of a quadrilateral are equal and parallel, the figure is a parallelogram. Let the opposite sides BC and AD of the quadrilateral ABCD be equal and parallel. *-, -7 Draw the diagonal...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 262 pages
...two equal triangles. 61. Cor. 2. Parallels included between parallels are equal. THEOREM XVIII. 65. If two sides of a quadrilateral are equal and parallel, the figure is a parallelogram. Let AB CD be a quadrilateral having B _ o BC equal and parallel to AD ; then / '\.' / AB CD is & parallelogram....
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...that is, the figure is a parallelogram (D. 28) ; which was to be proved. PROPOSITION XXX. THEOREM. If two sides of a quadrilateral are equal and parallel, the figure is a parallelogram. In the quadrilateral ABCD, let AB D_ be equal and parallel to DC: then will the figure be a parallelogram....
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...equal triangles. 61. Cor. 2. Parallels included between parallels are equal. THEOREM XVIII. (j.». If two sides of a quadrilateral are equal and parallel, the, figure is a paralldoijram. Let ABC D be a quadrilateral having BG BC equal and parallel to AD ; then /\~~ ~~7 A...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 pages
...are parallel. Therefore ABCD is a parallelogram. PROPOSITION XXXII.— THEOREM. 108. If two opposite sides of a quadrilateral are equal and parallel, the figure is a parallelogram. Let the opposite sides BC and AD of the quadrilateral ABCD be equal and parallel. *•, - -7 Draw the diagonal...
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