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To prove that ∆MP and ∆ONQ are congruent, we can use the Side-Angle-Side (SAS) congruence criterion.

Given: MP = NQ

We need to prove: 1) ∆MP ≅ ∆ONQ 2) MN and PQ bisect each other at O

Proof: 1) ∆MP ≅ ∆ONQ (using SAS congruence criterion) - Side MP = Side NQ (given) - Angle MPN = Angle QNO (corresponding angles) - Side MN = Side OQ (corresponding sides)

2) MN and PQ bisect each other at O - Since ∆MP ≅ ∆ONQ, we know that corresponding sides and angles are congruent. - Therefore, MN = OQ and PQ = NO. - This shows that MN and PQ bisect each other at O.

Thus, we have proven that ∆MP and ∆ONQ are congruent, and MN and PQ bisect each other at O.