Given a line segment AB, construct an isosceles triangle where the two congruent sides of the isosceles triangle have the same length as the length of AB.
Assuming that these axioms are true:

Question

Given a line segment AB, construct an isosceles triangle where the two congruent sides of the isosceles triangle have the same length as the length of AB. 
Assuming that these axioms are true:

anonymous · Answer

If I have to answer my problem using this axioms: 
(1) Any two points can be joined by a straight line
2) Any straight line segment can be extended indefinitely in a straight line.
(3) Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center
(4) All right angles are congruent
(5) Parallel postulate. If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.

anonymous · Answer

(6) Triangle Congruence. Let ABC and DEF be triangles. Assume that side AB is congruent to side DE, side BC is congruent to EF, and angle B is congruent to E.
Then triangle ABC is congruent to DEF