Question

The proof that ΔRST ≅ ΔVST is shown.

Given: ST is the perpendicular bisector of RV.
Prove: ΔRST ≅ ΔVST

Triangle R S V is cut by perpendicular bisector S T. Point T is the midpoint of line segment R V.

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

Answer 1

The missing reason is the perpendicular bisector theorem.

Since ST is the perpendicular bisector of RV, point S lies on that bisector, so S is equidistant from R and V. Hence RS ≅ VS.