¯¯¯

Question

is a perpendicular bisector of OR¯¯¯¯¯¯¯¯
and point S lies on the perpendicular bisector. The proof below proves that S is equidistant from both endpoints of OR¯¯¯¯¯¯¯¯
.

Statement Reason
1. TP¯¯¯¯¯¯¯
is a perpendicular bisector of OR¯¯¯¯¯¯¯¯
. given
2. OQ¯¯¯¯¯¯¯¯≅RQ¯¯¯¯¯¯¯¯
definition of a perpendicular bisector
3. ∠OQS
and ∠RQS
are right angles. definition of a perpendicular bisector
4. Right Angle Congruence Theorem
5. SQ¯¯¯¯¯¯¯≅SQ¯¯¯¯¯¯¯
Reflexive Property of Congruence
6. △OQS≅△RQS
SAS Congruence Theorem
7. SO¯¯¯¯¯¯¯≅SR¯¯¯¯¯¯¯
CPCTC Theorem

What is the missing statement in the proof?

(1 point)
Responses

∠OQS≅∠RQS
∠OQS≅∠RQS

∠QSO≅∠QSR
∠QSO≅∠QSR

∠QOS≅∠QRS
∠QOS≅∠QRS

∠OST≅∠RST
∠OST≅∠RST
Remaining Attempts : 3

Answer 1

The missing statement in the proof is:

∠OQS≅∠RQS

This is necessary to establish that the angles are congruent before applying the SAS (Side-Angle-Side) Congruence Theorem. So the completed proof would read:

Statement | Reason

1. TP¯¯¯¯¯¯¯ is a perpendicular bisector of OR¯¯¯¯¯¯¯. | given
2. OQ¯¯¯¯¯¯¯≅RQ¯¯¯¯¯¯¯¯. | definition of a perpendicular bisector
3. ∠OQS and ∠RQS are right angles. | definition of a perpendicular bisector
4. ∠OQS≅∠RQS | Right Angle Congruence Theorem
5. SQ¯¯¯¯¯¯¯≅SQ¯¯¯¯¯¯¯ | Reflexive Property of Congruence
6. △OQS≅△RQS | SAS Congruence Theorem
7. SO¯¯¯¯¯¯¯≅SR¯¯¯¯¯¯¯ | CPCTC Theorem

Thus, the answer is ∠OQS≅∠RQS.