Two-column Proof

Annie Fetter, The Geometry Forum

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 [For more discussions about two-column proofs, search the archives of the newsgroup geometry-pre-college for the words   two column proof   and browse the threads returned.] ```From: annie@mathforum.org (Annie Fetter) Subject: 2-column proof example Date: Wed, 25 Jan 1995 10:51:58 -0500 ``` ```Much as it pains me to do this :-) here's an example of a two column proof. The problem was one of our problems of the week last year. ********************************************************************** Problem of the Week for January 31 to February 4 (1994) Two engineers are scouting out an area where they plan to build a bridge. They are standing on the edge of the river, directly across from where the other end of the bridge will be. Their problem is this: They don't know how far it is across the river. They puzzle about this for a minute, and then Jill says to Jimmy, "I know how to find out how far it is." D Jill and Jimmy walk along the edge of the ----------------*-------- river to point B. Jimmy stays there. Then Jill walks to C, making sure that the distance river from B to C is equal to the distance from A to B. Then she turns 90 degrees, and walks ----*-----*-----*--------- away from the river until Jimmy, who is C| B A standing at B, is directly in line with D, | the point where they want the other end of | bridge. This is point E. Jill claims that | the distance from C to E is the same as the * distance from A to D. Is she right? Why E or why not? ********************************************************************** Given: BD = 3DAB,