Question

the proof that △rst ≅ △vst is shown.
given: st is the perpendicular bisector of rv.
prove: △rst ≅ △vst
what is the missing reason in the proof?

1. st is the perpendicular bisector of rv. (given)
2. ∠str and ∠stv are right angles. (def. of perpendicular bisector)
3. rs ≅ vs (?)
4. st ≅ st (reflexive property)
5. △rst ≅ △vst (hl theorem)

perpendicular bisector theorem
converse of the perpendicular bisector theorem
pythagorean theorem
sss congruence theorem

Explanation:

The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Here, since \(ST\) is the perpendicular bisector of \(RV\) and \(S\) is a point on \(ST\), by the perpendicular bisector theorem, \(RS = VS\).

Answer:

perpendicular bisector theorem