 | 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... | |
 | Joseph Claudel - Mathematics - 1906 - 758 pages
...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... | |
 | 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 - 329 pages
...other. Draw £7 ABCD as in § 107 ; and lines AC and BD. We then have : Given diagonals AC and BD of EH ABCD intersecting at E. To Prove AE = EC and BE =...; in like manner, AB = CD; then use § 106.) PROP. XXXYI. THEOREM 110. Two parallelograms are equal when two adjacent sides and the included angle of... | |
 | 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,...are equal when two adjacent sides and the included angle of one are equal respectively to two adjacent sides and the included angle of the other. b Draw... | |
 | Webster Wells - Geometry, Plane - 1908 - 208 pages
...centre of the parallelogram. PROP. XXXV. THEOREM 109. (Converse of Prop. XXXIII.) If the diagonal^ of a quadrilateral bisect each other, the figure is...by § 46 ; then AD = BC ; in like manner, AB = CD; tlieu use § 106.) PROP. XXXVI. THEOREM • ~j 110. Two parallelograms are equal when two adjacent... | |
 | Grace Lawrence Edgett - Geometry - 1909 - 104 pages
...included angle of one equal respectively to two adjacent sides and the included angle of the other. 3. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. 4. If two sides of a triangle are produced their own lengths through the common vertex, a line joining... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...Proof. BO = OD. Hyp. 2£a = 2£o'. §143 £& = £&'. § 65 .-.AOBF^AODE. §94 .-.EO=OF. §85 Ex. 32. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. Ex. 33. The diagonals of a rectangle are equal. PROPOSITION XLIII. _ THEOREM. 176. Two parallelograms... | |
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If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. 
