Ball, W. W. Rouse (Walter William Rouse), 1850-1925 · London, Macmillan and Co., limited · leaf 74
lacy *. To prove that , if two opposite sides of a quadrilateral are equal , the other two sides must be parallel. Let ABCD be a quadrilateral such that AB is equal to DC. Bisect AD in M, and through M draw MO at right angles to AD. Bisect BC in N, and draw NO at right angles to BC. If MO and NO… … diagram or outside the quadrilateral as in the right-hand diagram. Join 0A , OB, 0C, 0D. Since 0M bisects AD and is perpendicular to it, we have 0A = 0D, and the angle 0AM equal to the angle ODM. Similarly OB = 0C , and the angle OBN is equal to the angle OCN. Also by hypothesis AB = DC, hence, by…
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Internet Archive · University of Illinois Urbana-Champaign · Public domain (published before 1931). Free to use for anything.
