 | George Roberts Perkins - Geometry - 1860 - 472 pages
...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
...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
...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 - 472 pages
...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... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...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... | |
 | 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... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...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... | |
 | Edward Olney - 1872 - 270 pages
...with AD and BC. Therefore, AD is parallel to BC FIG. 180 <i. ED PROPOSITION X. 240. Theorem.—If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. DEM.—In (a) let AB = DC, and AD = BC; then is ABCD a parallelogram. For, divide the quadrilateral... | |
 | 1873 - 192 pages
...at unequal distances from the perpendicular, the more remote is the greater. 3. Prove that when the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 4. Two angles of a triangle being given, to find the third by geometric construction. 5. What is the... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...the two diameters of a parallelogram be drawn, it will be divided into four equal parts. 35. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 36. If the opposite angles of a quadrilateral are equal, the figure is a parallelogram. 37. If the... | |
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If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 
