Given that AP is perpendicular to AB, is perpendicular to BQ and AP is congruent to BQ, which of the following proves that O is the midpoint of AB and PQ?

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Option A:

1. AP is congruent to BQ (Given)
2. AP is perpendicular to AB, BQ is perpendicular to AB (Given)
3. m
6. Triangle OAP is congruent to Triangle OBQ (CPCTC)
7. AO is congruent to BO, PO is congruent to OQ (CPCTC)
8. AO is congruent to BO, PO is congruent to OQ (Def. of congruence)
9. O is the midpoint of AB and PQ (Def of midpoint)

Option B:

1. AP is congruent to BQ (Given)
2. AP is perpendicular to AB, BQ is perpendicular to AB (Given)
3. m
6. Triangle OAP is congruent to Triangle OBQ (AAS Steps 4,5, 1)
7. AO is congruent to OP, BO is congruent to OQ (CPCTC)
8. AO = OP, BO =OQ (Def. of congruence)
9. O is the midpoint of AB and PQ

Option C:

1. AP is congruent to BQ (Given)
2. AP is perpendicular to AB, BQ is perpendicular to AB (Given)
3. m
4. AO is congruent to OB (Supp
5. Triangle AOP is congruent to BOQ (SAS Steps 1, 5, 4)
6. AO is congruent to OP, BO is congruent to OQ (CPCTC)
7. AO=OP, BO =OQ (Def of congruence)
8. O is the midpoint of AB and PQ (Def of midpoint)

Option D:

1. AP is congruent to BQ (Given)
2. AP is perpendicular to AB, BQ is perpendicular to AB (Given)
3. m
6. Triangle AOP is congruent to Triangle BOQ (SAS Steps 1, 5, 4)
7. AO is congruent to BO, OP is congruent to OQ (CPCTC)
8. AO=BO, BO - OQ (Def. of congruence)
9. O is the midpoint of Ab and PQ (def of midpoint)