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" If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. "
Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ... - Page 5
by Harvard University - 1899 - 31 pages
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 238 pages
...sides AD, BC, are parallel (Th. xiii). For a like reason DC is parallel to AB, and the figure ABCD is a parallelogram. THEOREM XXV. If two opposite sides of a quadrilateral are equal and parallel, the remaining sides will also be equal and parallel, and the fgure will be a parallelogram. Let ABCD be...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...sides AD, BC, are parallel (Th. xiii). For a like reason DC is parallel to AB9 and the figure ABCD is a parallelogram. THEOREM XXV. If two opposite sides of a quadrilateral are < the remaining sides will also be equal and parallel, and the figur will be a parallelogram. Let ABCD...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 474 pages
...before, AD and BC are parallel. Consequently the figure is a parallelogram (D. XXV.). THEOREM XXIX. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. If we suppose AB = DC, and AD = BC, and draw the diagonal BD, we shall have the three sides of the...
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...figure symmetrically, because the position of the sides of the triangles is reversed. 359. Theorem. — If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. Join AC. Then, the triangles ABG and CDA are equal. For the side AD is AB equal to BC, and DC is equal...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 438 pages
...figure symmetrically, because the position of the sides of the triangles is reversed. 359. Theorem. — If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. Join AC. Then, the triangles ABC and CDA are equal. For the side AD is equal to BC, and DC is equal...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1870 - 394 pages
...sides AD, BC, are parallel (Th. xiii). For a like reason DC is parallel to AB, and the figure ABCD is a parallelogram. THEOREM xxv. If two opposite sides of a quadrilateral are equal and parallel, the remaining sides will also be equal and parallel, and theßgvre vñll be a parallelogram. Let ABCD be...
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Treatise on Plane and Solid Geometry for Colleges, Schools, and Private Students

Eli Todd Tappan - Geometry - 1873 - 288 pages
...figure symmetrically, because the position of the sides of the Uiangles is reversed. 359. Ttccrem — If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. Join AC. Then, the triangles ABC and CDA arc equal. For the side AD is equal to BC, and DC is equal...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 262 pages
...reference to (79) ; then that the triangles are equal by (40) or (41). 82. (Converse of part of 62.) If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 83. (Converse of part of 62.) If the opposite angles of a quadrilateral are equal, the f)gure is a...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 562 pages
...and BC. 4. s. D. Fio. 180 Therefore, AD is parallel to BC (152). PROPOSITION X. 240. Jlieoreni. — If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. DEM.— In («) let AB = DC, and AD = BC ; then is ABCD a parallelogram. For, divide the quadrilateral...
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...reference to (79) ; then that the triangles are equal by (40) or (41).. 82. (Converse of part of 62.) If the opposite sides of a quadrilateral are equal, 'the figure is a parallelogram. 83. (Converse of part of 02.) If the opposite angles of a quadrilateral are equal, the figure is a...
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