The proof that δrst ≅ δvst is shown. given: st is the perpendicular bisector of rv. prove: δrst ≅ δvst what is the missing reason in the proof? statements reasons 1. st is the perpendicular bisector of rv. 1. given 2. ∠str and ∠stv are right angles. 2. def. of perpendicular bisector 3. rs ≅ vs 3. ? 4. st ≅ st 4. reflexive property 5. δrst ≅ δvst 5. hl theorem perpendicular bisector theorem converse of the perpendicular bisector theorem pythagorean theorem sss congruence theorem

Refer to the attached image.

To prove:  ΔRST ≅ ΔVST

Statement                                                                  Reason

1. ST is the perpendicular bisector of RV.    1. Given

2. ∠STR and ∠STV are right angles.              2. def of perpendicular bisector

3. RS ≅ VS                                                   3. Perpendicular bisector theorem

As Perpendicular bisector theorem states that "If a point is on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints"

Since, S is on the perpendicular bisector of segment RV, then it is equidistant from the segment's endpoints that is R and V.

Therefore, RS ≅ VS.

4. ST ≅ ST                                                  4. reflexive property

5. ΔRST ≅ ΔVST                                          5. HL theorem

Hence proved,  ΔRST ≅ ΔVST.

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