 | Euclid - Euclid's Elements - 1904 - 488 pages
...right angle, all its angles are right angles. 5. The diagonals of a parallelogram bisect each other. 6. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. 7. If two opposite angles of a parallelogram are bisected by the diagonal which joins them, the figure... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...angles of one are equal to three sides and the two included angles of the other, respectively. Ex. 33. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. Ex. 34. Lines joining the midpoints of the sides of a rectangle in order form a rhombus. Ex. 35. Lines... | |
 | William Chauvenet - 1905 - 336 pages
...+ / B + /_ BCA = 2rt. /._. Prop. XXVL /_ BCD = / A + /_ B. QED (4) EXERCISE 3, PAGE 43.—THEOREM. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. ..-.-''B'-. In the ^ AEB and CMD »e have CE — EB, Hyp. ED = AE, Hyp. / CED = /_ AEB. Prop. V. &AEB... | |
 | Joseph Claudel - Mathematics - 1906 - 758 pages
...bisects the angle at the vertex. Fig. 44 Fig. 45 660. The diagonals of a parallelogram bisect each other; conversely, if the diagonals of a quadrilateral bisect each other, the figure is a parallelogram (Fig. 44). Besides these properties of a parallelogram : 1st. The diagonals of a rectangle are equal... | |
 | International Correspondence Schools - Building - 1906 - 634 pages
...(Art. 37). Therefore, the triangles are equal (Art. 72) and OA = OC, OB = O D. PIG. 68 1. Show that if the diagonals of a quadrilateral bisect each other the figure is a parallelogram. SUGGESTION.— In Fie. 68, assume that OA — O C. OB =O D. Then show that triangle BOC = triangle... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...angle ? 122 If one angle of a parallelogram is a right angle, the figure is a right parallelogram. 123 If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. [A AOD = A BOC (§ 162). /. AD = BC, and Z1=Z2 (§166). /. AD is || to BC (§ 125). .-. ABCD is a O... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...Z c = Z r (?) (97). .-. A FXG = A EXH (?) (54). .-. FX = XH and Gx = XE (?) (27). QED 138. THEOREM. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. Given: (?). To Prove: (?). Proof: In A FXG and EXH show three parts of one = etc. Hence certain A are... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...c = Z r (?) (97). ... A tfXG = A EXH (?) (54). ... FX = XH and GX = XE (?) (27). QED 138. THEOREM. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. . Given: (?). To Prove: (?). Proof: In A FXG and EXH show three parts of one = etc. Hence certain A... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...point E is called the centre of the parallelogram. PROP. XXXV. THEOREM 109. (Converse of Prop. XXXIII.) If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. To Prove ABCD a O. (Prove A AED = A BEC, by § 46 ; then AD = BC ; in like manner, AB — CD; then... | |
 | Webster Wells - Geometry, Plane - 1908 - 206 pages
...point E is called the centre of the parallelogram. PROP. XXXV. THEOREM 109. (Converse of Prop. XXXIV.) If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. To Prove ABCD a O. (Prove A AED = A BEC, by § 46 ; then AD = BC ; in like manner, AB = CD; then use... | |
| |
If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. 
