 Hello friends, welcome to the session. I am Alkaal. Let's discuss a given question that is diagonals AC and BD of adripezium A, B, C, D with AB parallel to DC intersect each other at O. Using a similarity criteria for two triangles show that OA upon OC is equal to OB upon OD. Here is the figure according to the question where AB, CD is adripezium and AC and BD are diagonals which are intersecting at the point O and AB is parallel to CD. Now let's begin with the solution. We are given AB is a adripezium. AB is parallel to DC. Now we have to show that OA upon OC is equal to OB upon OD. Now let's see the proof in triangle OA, V and triangle OC, D. In triangle OA, V, triangle OC, D, we see that angle AOB is equal to angle COD since they both are vertically opposite angles. Therefore we can say that angle AOV is equal to angle COD since they are vertically opposite to angle OC because they are alternate angles since AB is parallel to DC. So we will say angle OAB is equal to angle OC, D. Alternate angles AB is parallel to DC. Similarly, angle OBA is equal to angle ODC. They are also alternate angles as AB is parallel to DC. So we will write angle OBA is equal to angle ODC. Again, alternate angles AB is parallel to DC. We can say that the triangle OAV is similar to triangle ODC by AAA criteria of similarity. So we will write triangle OAV is similar to triangle ODC by criteria. So now in case of two similar triangles we know that the ratio of their corresponding sides are equal. So this implies that OA upon OC is equal to OB upon OD. So this is proved. Hope you understood it and enjoyed the session. Goodbye and take care.