 Hello and welcome to the session. In this session we will discuss site splitting theorem. Now, statement of site splitting theorem says, a line parallel to a site of a triangle that intersects the other two sites in distinct points divides those two sites proportionally that is in the given triangle PQR it is given that DE is parallel to QR then PD upon DQ will be equal to PE upon ER Now we are going to prove this theorem. Now in triangle PDE and triangle PQR it is given that DE is parallel to QR so here angle PDE will be equal to angle PQR since they are corresponding angles also angle PED will be equal to angle PRQ that is this angle is equal to this angle since they are corresponding angles angle PE that is angle DPE will be equal to angle QPR that is the common angle SO by AAA rule that is angle angle angle rule we say that triangle PDE is similar to triangle PQR we know that if two triangles are similar then their corresponding sites are proportional so here PQ upon PDE will be equal to PR upon PE and this is equal to QR upon DE now taking these first two ratios we have now PQ can be written as PD plus DEQ whole upon PD and this is equal to now PR can be written as PE plus ER and this whole upon PE this further implies that PD upon PD plus DEQ upon PD is equal to PE upon PE plus ER upon PE that implies that 1 plus DEQ upon PD will be equal to 1 plus ER upon PE and this further implies that DEQ upon PD is equal to ER upon PE now taking reciprocal on both sites we get PD upon DEQ is equal to PE upon ER hence we have proved the required result now let us discuss an example given triangle PQR find ER let us start with the solution of this example here we are given triangle PQR where DE is parallel to QR also PD is equal to 10 PE is given as 12 and DEQ is given as 6 and we have to find ER since DE is parallel to QR so by side splitting theorem we have PD upon DEQ is equal to PE upon ER now substituting all these values here we get 10 upon 6 is equal to 12 upon ER this implies that ER is equal to 12 into 6 whole upon 10 on solving we get ER is equal to 72 by 10 that is equal to 7.2 thus ER is equal to 7.2 thus in this session we have learnt side splitting theorem this completes our session hope you enjoyed this session