 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...diagonal BD. AABD=ABCD. (?) , Whence AB — CD. Prove ABCD a parallelogram. [§ 195. Converse.] QED PROPOSITION XXXV. THEOREM 207. The diagonals of a...bisect each other, the figure is a parallelogram. Let A BCD be a parallelogram, DB and AC its diagonals. To Prove BO = OD and AO = OC. Proof. Prove A ROC—... | |
 | Arthur Schultze - 1901 - 260 pages
...HINT.—Prove the equality of a pair of alternate interior angles by means of equal triangles. Ex. 192. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. PROPOSITION XXXIV. THEOREM 139. If two sides of a quadrilateral are equal and parallel, the figure... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...XXI. C. 1) ; and the same may be shown for each of the other angles. PROPOSITION XXXIII. — THEOREM. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. Given. — Let the diagonals, AC and BD, of the quadrilateral ABCD, bisect each other in E. To Prove.... | |
 | Arthur Schultze - 1901 - 392 pages
...— Prove the equality of a pair of alternate interior angles by means of equal triangles. Ex. 192. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. PROPOSITION XXXIV. THEOREM 139. If two sides of a quadrilateral are equal and parallel, the figure... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...— Prove the equality of a pair of alternate interior angles by means of equal triangles. Ex. 192. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. PROPOSITION XXXIV. THEOREM 139. If two sides of a quadrilateral are equal and parallel, the figure... | |
 | James Howard Gore - Geometry - 1902 - 266 pages
...triangles are therefore equal (by 88) in all their parts, or BO = OE and AO = OG. QED EXERCISES. 1. Show conversely, if the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. 2. Show that the diagonals of a rhombus bisect each other at right angles. 3. Show that the diagonals... | |
 | Michigan. Department of Public Instruction - Education - 1902 - 330 pages
...this era. GEOMETRY. tNumber each step; state all the reasons in full; omit any two marked*.) 1. 1f the diagonals of a quadrilateral bisect each other the figure is a parallelogram. 2. Name and define the different kinds of quadrilaterals. Show that the straight line joining the non-parallel... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...(Theorem XVIII), and AE = EC, and BE = ED (homologous sides of equal triangles) . THEOREM XXXII. 111. Conversely, if the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. Let the diagonals of the quadrilateral ABCD bisect each other at E. To prove that the figure is a parallelogram.... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 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... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...difference of the base angles. Let ZB be greater than Z A. Z DCE = 90° - Z .4 - Z ACD. -1ZB. Ex. 68. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. Prove AA OB = A COD. Ex. 69. The diagonals of a rectangle are equal. Prove A ABC = A BAD. Ex. 70. If... | |
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If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. 
