 Hello and welcome to the session. In this session we discussed the following question which says, in the given figure, PQR is an isosceles triangle in which PQ is equal to PR. If PQ and PR are produced to S and T respectively, such that QS is equal to RT, prove that QT is equal to RS. First we shall recall the SAS congruence condition according to which we have that two triangles congruent if the two sides and the included angle of one are respectively equal to the two sides and the included angle of the other. This is the key idea for this question. Now we move on to the solution. This is the figure given to us in which we have a triangle PQR in which PQ is equal to PR as PQR is an isosceles triangle. Then the side PQ of triangle PQR is produced to S and side PR of triangle PQR is produced to T and we have QS is equal to RT. And we need to prove that QT is equal to RS. So we shall consider the triangles PRS and PQT. In these two triangles we have PQ equal to PR. It's given to us then angle P is equal to angle P. It's a common angle to both the triangles. Now we have PQ is equal to PR and also QS is equal to RT. Therefore PQ plus QS is equal to PR plus RT. From the figure we have PQ plus QS is equal to PS and PR plus RT is equal to PT. Therefore this implies that PS is equal to PT. So for the triangles PRS and PQT PQ is equal to PR given to us angle P is equal to angle P. It's a common angle and PS is equal to PT. Therefore we have triangle PRS is congruent to the triangle PQT by SAS congruence condition that we have stated in the key idea. Now since both these triangles are congruent so this implies that QT is equal to RS that is CPCT. They are the corresponding parts of congruent triangles so they are equal. And we were supposed to prove this only. So hence proved this completes the session. Hope you have understood the solution for this question.