Question

A conjecture and the two-column proof used to prove the conjecture are shown. Given: S is the midpoint of segment R T. Segment R T is congruent to segment X Y. Prove: segment R S is congruent to segment X Y. Segment X Y with endpoints X and Y. Line R S T is horizontal. Line R S T has two segments R S and S T with the same length. S is the midpoint and R and T are the extreme left and extreme right points respectively. Drag an expression or phrase to each box to complete the proof.

Answer 1

given: s is the midpoint of rt

definition of midpoint: rs st

given: st xy

transitive property of congruence: rs xy

Answer 2

Answer:

  Statement                            Reason

1. S is the midpoint of RT        Given

2. RS ≅ ST                              Definition of midpoint

3. ST ≅ XY                              Given

4.  RS ≅ XY                              Transitive property of congruence

(I'm assuming there is a mistype in the question,where it says RT is congruent to segment XY, I suppose it was ST is congruent, otherwise RS cannot be  congruent to segment XY)