 | Arthur Schultze - Mathematics - 1912 - 398 pages
...the textbook and every original should be so attacked, ie analyzed. Thus in teaching the proposition, "If the opposite sides of a quadrilateral are equal, the figure is a parallelogram," we should ask, What is the usual method of demonstrating the parallelism of lines ? And after the original... | |
 | Arkansas Education Association - Education - 1912 - 270 pages
...principles he has had for the cue to the proof of the new theorem. Suppose that he is required to prove, "If the opposite sides of a quadrilateral are equal, the figure is a parallelogram." When we come to this in our text we have had only one test for a parallelogram, viz.: the definition... | |
 | University of Calcutta - 1912 - 746 pages
...The opposite sides and angles of a parallelogram are equal ; and 7 its diagonals bisect each other. If the opposite sides of a quadrilateral are equal, the figure is a 6 parallelogram. 8. In any triangle, the square on the side subtending an acute 8 angle is less than... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...diagonals of a parallelogram are equal, the figure is a rectangle. PROPOSITION XXXIV. THEOREM 146. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. B— Given quadrilateral A BCD, with AB = CD; AD = BC. To prove AD II BC; AB II CD. Ex. 347. If the... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...be said of all points in AB with respect to their distance from CD * PROPOSITION XXVII. THEOREM 129. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. Given the quadrilateral ABCD, having BC equal to AD, and AB equal to DC. To prove that the quadrilateral... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...diagonals of a parallelogram are equal, the figure is a rectangle. t PROPOSITION XXXIV. T REOREM 146. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. B . Given quadrilateral ABCD, with AB = CD; AD = BC. To prove AD II BC; AB II CD. Ex. 347. If the four... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...dropped from any points in _ AB to CD (§ 127) ? Hence what may " CD~ PROPOSITION XXVII. THEOREM 129. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. Given the quadrilateral ABCD, having BC equal to AD, and AS equal to DC. To prove that the quadrilateral... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 280 pages
...diagonal of a parallelogram divides it into two congruent triangles. PROPOSITION XXXIX. THEOREM 128. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. [Converse of 124.] Given : Quadrilateral ABCD ; AB = DC; AD=BC. To Prove : ABCD is a O. Proof : Draw... | |
 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 250 pages
...parallelogram ABCD, BE and DF are perpendicular to the diagonal AC. Prove that BE = DF. 244. THEOREM. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. FIG. 106. (The proof is left to the student.) SUGGESTION : Draw a diagonal BD. A ABD = A CBD. Show... | |
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If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 
