 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 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... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...BDC are equal ; therefore AB is parallel to DC (56), and ABCD is a parallelogram. THEOREM XXYI. 121 1 If the opposite sides of a quadrilateral are equal the figure is a parallelogram. Let ABCD be a quadrilateral hav- S _ O ing AB=DC and BC = AD; then /\~ ~~7 ABCD is a parallelogram. / NX\... | |
 | Edward Olney - 1879 - 278 pages
...made by AC with AD and BC. Therefore, AD is parallel to BC (149). QED PROPOSITION X. 24O. 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... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...and ¿- a = Z. b; (Hyp.) AABD = &EFH. (83) But these As are the halves of the CUs. THEOREM XLII. 132. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. In the quadrilateral AB CD, let AB = CD, and AC= BD. С D A To prove that AB С D is a EH. Draw the... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...3. If one angle of a parallelogram is a right angle, all the others are right angles. THEOREM XXIV. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. For, draw the diagonal BD; then the triangles ABD and BDC have /e '' angle a equals its alternate angle... | |
 | Edward Olney - Geometry - 1883 - 344 pages
...by hypothesis, the quadrilateral is a parallelogram (233). Q- ED PROPOSITION X. 248. Theorem.—If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. DEMONSTRATION. Let ABCD, (a), be a quadrilateral, having AD = BC and AB .. DC. We are to prove that... | |
 | George Albert Wentworth - Geometry - 1885 - 424 pages
...figure ABCE is a O, § 125 PROPOSITION XLI. THEOBEM. 137. If in a quadrilateral the opposite sides be equal, the figure is a parallelogram. Let the figure ABCE be a quadrilateral having BC = AE and.AB = EC. We are to prove figure ABC E a O. Draw A C. In the A ABC and A EC BC = AE, Hyp. AB... | |
 | William Chauvenet - Geometry - 1887 - 342 pages
...opposite sides of a quadrilateral are equal and parallel, the figure is a parallelogram. PROPOSITION XXXI. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. SYLLABUS TO BOOK I. POSTULATES, AXIOMS, AND THEOEEMS. POSTULATE I. Through any two given points one... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...opposite sides of a quadrilateral are equal and parallel, the figure is a parallelogram. PROPOSITION XXXI. If the opposite sides of a quadrilateral are equal, the figure Is a parallelogram. PROPOSITION XXXII. The diagonals of a parallelogram bisect each other. BOOK II. PROPOSITIONS. POSTULATE.... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...equal, the lines are parallel). .-. the figure ABCE is a O, § 168 PROPOSITION XXXIX. THEOREM. 183. // the opposite sides of a quadrilateral are equal, the...parallelogram. Let the figure ABCE be a quadrilateral having BO = AE and AB = EC. To prove figure A£CE a dJ. Proof. Draw AC. In the A ABC and AEC £C= AE, Hyp.... | |
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If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 
