the proof that $ \triangle rst \cong \triangle vst $ is shown.
given: $ \overline { st } $ is the perpendicular bisector of $ \overline { rv } $.
prove: $ \triangle rst \cong \triangle vst $
what is the missing reason in the proof?
| statements | reasons |
| --- | --- |
| 1. $ \overline { st } $ is the perpendicular bisector of $ \overline { rv } $. | 1. given |
| 2. $ \angle str $ and $ \angle stv $ are right angles. | 2. def. of perpendicular bisector |
| 3. $ \overline { rs } \cong \overline { vs } $ | 3. ? |
| 4. $ \overline { st } \cong \overline { st } $ | 4. reflexive property |
| 5. $ \triangle rst \cong \triangle vst $ | 5. hl theorem |
perpendicular bisector theorem
converse of the perpendicular bisector theorem
pythagorean theorem
sss congruence theorem

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Accepted Answer

# Brief Explanations:
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 $ST$ is the perpendicular bisector of $RV$ and $S$ is a point on $ST$, by the perpendicular bisector theorem, $RS\cong VS$.

# Answer:
perpendicular bisector theorem

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QUESTION IMAGE

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Explanation:

Answer:

statements	reasons
2. \\( \angle str \\) and \\( \angle stv \\) are right angles.	2. def. of perpendicular bisector
3. \\( \overline { rs } \cong \overline { vs } \\)	3. ?
4. \\( \overline { st } \cong \overline { st } \\)	4. reflexive property
5. \\( \triangle rst \cong \triangle vst \\)	5. hl theorem