# Thread: Proof of congruent triangle construction

1. ## Proof of congruent triangle construction

Theorem: Given triangle ABC, segment DE such that DE = AB, and H is a half-plane bounded by the line DE, then there is a unique point F that is an element of H such that triangle DEF is congruent to triangle ABC.

What I have so far:
Givens stated above. By the protractor postulate, there exists a unique ray -DG-> such that G is in H and <BAC = <EDG. By the ruler postulate, there must be a point F on -DG-> such that DF=AC. Thus by Side-Angle-Side, triangles ABC and DEF are congruent.

How do I go about proving the uniqueness of F though??

2. Originally Posted by spectralsea
Theorem: Given triangle ABC, segment DE such that DE = AB, and H is a half-plane bounded by the line DE, then there is a unique point F that is an element of H such that triangle DEF is congruent to triangle ABC.

What I have so far:
Givens stated above. By the protractor postulate, there exists a unique ray -DG-> such that G is in H and <BAC = <EDG. By the ruler postulate, there must be a point F on -DG-> such that DF=AC. Thus by Side-Angle-Side, triangles ABC and DEF are congruent.

How do I go about proving the uniqueness of F though??
What are the exact words of the "ruler postulate"? Doesn't it include the uniqueness, as well as the existence, of the point?