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

Question

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

Accepted Answer

# Explicación breve:
El teorema del bisector perpendicular establece que si un punto está en el bisector perpendicular de un segmento, entonces está equidistante de los extremos del segmento. En este caso, $ S $ está en el bisector perpendicular $ \overline{ST} $ de $ \overline{RV} $, por lo que $ RS = VS $.

# Respuesta:
perpendicular bisector theorem

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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