In trapezium `PQRS`, `PQ||SR`. If `PQ=4` units , `SR=6`units . If the diagonals of the trapezium intersect each other at the points `C`, then find the ratio `CQ:CS`.

Explanation

In `DeltaPCQ` and `DeltaSCR`, `/_PCQ=/_SCR` [`:'` opposite angles]
`/_PQC=/_RSC`[`:'` alternate angle]
`:.DeltaPCQ~DeltaSCR`
`:.(PQ)/(SR)=(CQ)/(CS)` [by Thales' theorem]
or, `(4"units")/(6"units")=(CQ)/(CS)` or, `(2)/(3)=(CQ)/(CS)` or, `CQ:CS=2:3`
Hence the ratio `CQ:CS=2:3`