Draw a point separate from segment AB and name it C.

Open your compass to the width of AB.

Without changing the width, place the compass point on point C and draw an arc.

Use a straightedge to draw a line between point C and the arc.

Name the intersection of the line and the arc D. CD is the congruent segment.

Set the compass point on Point A and open it more than halfway across AB.

Use the existing compass width to draw an arc that goes above and below AB that is centered on A.

Place the compass point on Point B without changing the width, and repeat Step 2 to create another arc that is centered on B.

Name the intersections of the arcs C and D.

Use a straightedge to draw the line through point C and D and label the point of intersection P.