 | Nicholas Tillinghast - Geometry, Plane - 1844 - 110 pages
...AD to BC (Prop. 10), and the figure is a parallelogram. PROP. XXVI. THEOREM. If two of the opposite sides of a quadrilateral are equal and parallel, the other two sides will be equal and parallel, and the figure will be a parallelogram. In the quadrilateral ABCD (preceding... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...is a parallelogram. Therefore, if the opposite sides, &c. PROPOSITION XXXI. THEOREM. If two opposite sides of a quadrilateral are equal and parallel, the other two sides are equal and parallel, and the figurt is a parallelogram. sides AB, CD equal and parallel; then will V~~ ~~/\ the sides AC, BD be... | |
 | George Roberts Perkins - Geometry - 1860 - 472 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... | |
 | 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... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...AC with AD and BC. Therefore, AD is parallel to BC (152) 4. ED '' PROPOSITION X. 240. Theorem.—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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If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 
