Question

the proof that δrst ≅ δvst is shown.
given: overline{st} is the perpendicular bisector of overline{rv}.
prove: δrst ≅ δvst
what is the missing reason in the proof?
statements reasons

1. overline{st} is the perpendicular bisector of overline{rv}. 1. given
2. ∠str and ∠stv are right angles. 2. def. of perpendicular bisector
3. overline{rs} ≅ overline{vs} 3. ?
4. overline{st} ≅ overline{st} 4. reflexive property
5. δrst ≅ δvst 5. hl theorem

options:

• 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 \(S\) is on the perpendicular bisector \(\overline{ST}\) of \(\overline{RV}\), by the perpendicular bisector theorem, \(\overline{RS}\cong\overline{VS}\).

Answer:

perpendicular bisector theorem