| George Roberts Perkins - Geometry - 1856 - 235 pages
...IV.), true for all quadrilaterals. Now, if we suppose A = C, and B = D, we shall find 2 A + 2D z B = **4 right angles, or A + D = 2 right angles, hence AB...opposite sides of a quadrilateral are equal, the figure** isa parallelogram. If we suppose AB = DC, and AD = BC, and draw the diagonal BD, we shall have the... | |
| Eli Todd Tappan - Geometry, Modern - 1864 - 292 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 - 436 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 - 566 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 - 238 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... | |
| 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... | |
| Edward Olney - 1872 - 270 pages
...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 - 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... | |
| 1873 - 164 pages
...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 - Euclid's Elements - 1874 - 349 pages
...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... | |
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