Question

Show that AO=OQ and BO = OP.Please help me as fast as possible....​

Answer 1

AB=PQ (given)
ABO=POQ (alternate angles)

Explanation:

AB=PQ (given)
ABO=POQ (alternate angles)
but i lose to find AO=OQ and BO=OP

Answer 2

Given:

• AB ║ PQ,
• AB = PQ.

Since AB and PQ are parallel and AQ is transversal:

• ∠BAQ ≅ ∠PQA as alternate interior angles.

Since AB and PQ are parallel and BP is transversal:

• ∠ABP ≅ ∠QPB as alternate interior angles.

This gives us:

• ΔABO ≅ ΔQPO as per ASA (angle-side-angle)

Since the triangles are congruent, their corresponding sides are congruent too:

• AO = OQ,
• BO = OP