Question

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

Explanation:

Step1: Understand the perpendicular bisector theorem

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.

Step2: Apply the theorem to the problem

Since \(ST\) is the perpendicular bisector of \(RV\) (given), and \(S\) is a point on \(ST\), by the perpendicular bisector theorem, \(RS\cong VS\).

Answer:

perpendicular bisector theorem