# <span lang="EN-US

Given: PA AB, QB AB and PA=QB

To prove: AO = OB and PO = OQ

It is given that PA AB and QB AB.

This means that ∆PAO and ∆QBO are right angled triangles.

It is also given that PA=QB

Now in ∆PAO and ∆QBO,

OAP = OBQ = 90°

PO = OQ

Hence by hypotenuse-leg congruency,

∆PAO QBO

AO = OB and PO = OQ ….by cpct

Hence proved that AO = OB and PO = OQ

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