 | George Roberts Perkins - 1860 - 472 pàgines
...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 - 1864 - 288 pàgines
...figure symmetrically, because the position of the sides of the triangles is reversed. 359. Theorem. — If the opposite sides of a quadrilateral are equal,...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 /— j to AB, by hypothesis;... | |
 | Eli Todd Tappan - 1868 - 444 pàgines
...figure symmetrically, because the position of the sides of the triangles is reversed. 359. Theorem. — If the opposite sides of a quadrilateral are equal,...parallelogram. Join AC. Then, the triangles ABC and CDA are equal. For the side AD is equal to BC, and DC is equal /- j to AB, by hypothesis; and p Q they... | |
 | Edward Olney - 1872 - 562 pàgines
...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 - 1872 - 124 pàgines
...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... | |
 | William Frothingham Bradbury - 1872 - 262 pàgines
...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 - 1872 - 270 pàgines
...AC 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... | |
 | Edward Olney - 1872 - 472 pàgines
...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... | |
 | 1873 - 192 pàgines
...drawn 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 - 1874 - 400 pàgines
...34. If 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... | |
| |
If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 
