Date: Feb 1, 1994 3:18 PM
Author: Problem of the Week
Subject: Problem of the Week, January 31-February 4

Sorry for the puzzle being a day late!  -Annie

The problem of the week is a regular feature here at the geometry forum.
Each weekend a high school level geometry problem will be posted, and the
following weekend a summary of solutions and their authors will be posted.

Please do not post solutions to the problem of the week; instead mail your
answer along with as detailed a description of your method as
necessary/possible to (replying to this message
will also work). Solutions should be received by midnight Friday so they
can be combined and posted over the weekend.

Please include your name, grade, and school along with your answer.

Problem of the Week for January 31 to February 4

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?