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.