 Hello and welcome to the session. Let's work out the following problem. It says in figure one This is a figure one ABCB is a trapezium in which AB is parallel to DC The diagonals AC and BD intersect at O prove that A O upon OC A O upon OC is equal to B O upon OD. So let's now move on to the solution Let's first write what is given to us. We are given a trapezium in which AB is parallel to DC and The diagonals intersect at O Let's now write what we have to prove We have to prove that A O upon OC is equal to B O upon OD Let's now do some construction now draw OM parallel to AB and Since AB is parallel to DC. So OM is parallel to DC this is the line OM which is parallel to AB and DC. So let's now start the proof now in triangle ADC OM is parallel to DC therefore by basic proportionality theorem AM upon MD is equal to A O upon OC by B P T The basic proportionality theorem Now in triangle ADV OM is parallel to AB by construction. So again by B P T AM upon MD is equal to B O upon OD Right, let's name this as to now. We have got that AM upon MD is equal to A O upon OC Also, AM upon MD is equal to B O upon AB. So from 1 and 2 we have A O upon OC A O upon OC is equal to B O or OD upon DO Hence proved So in such questions do remember to use the basic proportionality theorem like Constructing the line parallel to one of the side of the triangle. So bye for now. Take care. Have a good day