Constructing a Triangle Given Three Line
Segments

Suppose you are given three
line segments,

and you are asked to
construct the triangle with theses segments as the lengths of the sides. How do you do this? Here is one way.

Begin by constructing a circle
with a center, A, and radius *j*. Construct the line segment between the
two. Then choose a point on the
circle, B, and construct the line segment between them. This line segment is congruent to *j.*

Now construct a circle with
center B and radius *k*, and a
circle with center A and radius *l*. Call the intersection of these two
circles C.

Construct the line segment
BC. This line segment is congruent
to *k*.

Construct the line segment
AC. This line segment is congruent
to *m.*

Now hide the circles. If you measure the lengths you can see
that the triangle is made of the given segments.

Of course, measurement is not
a proof, but it is a nice confirmation that you got what you wanted.