Constructing a Triangle

Date: 08/20/99 at 20:47:33
From: angel
Subject: Geometry

How do you construct a triangle with 3 different size segments, or the 
same size segments?

Date: 08/20/99 at 23:21:37
From: Doctor Peterson
Subject: Re: Geometry

Hi, Angel.

Here's a quick way to do this with compass and straightedge. Make a 
line and measure out the three lengths, a, b, and c, along it, one 
after the other. Then use a compass to draw a circle at each of the 
two places where two of these segments meet (C and A), with the radius 
set to the length of the "outer" segment (a or c respectively), so 
that the circles pass through the outer ends of the segments (X and 
Y). Where these circles meet (if at all) is the third vertex of the 
triangle, B. Connect B to A and C to make the triangle, and you're 
done.

   

If the sides are the same length, you just have to draw one copy, 
segment AB. See if you can figure out how to make the circles in that 
case.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/