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

Answer 1

A. Perpendicular bisector theorem

Explanation:

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Answer 2

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.