 Hi and welcome to the session. Let us discuss the question it says show that of all line segments drawn from a given point not on it the perpendicular line segment is the shortest. Now in this question we need to first draw a figure that will make the question more understandable. It says that let from point P there is one perpendicular line on the line L and there is one slanting line Pn. Let this be Pn. So we are given in the question that a straight line L and a point P not lying on L also Pn is perpendicular to L and N is any point on L other than right. So this describes the question we have shown that of all the line segments drawn from a given point we have just taken two line segments from a given point. One is perpendicular and one is not perpendicular. We need to show that the perpendicular line is the shortest that means Pm is smaller than Pm. So we need to prove that Pm is smaller than Pn right. So let us start with our proof. Now in triangle we have angle M equal to 90 degrees. Therefore that implies that angle N has to be less than 90 degrees because the sum of angle P and N has to be 90 degrees and angle M one of the angle is equal to 90 degrees right. Now we also have that angle P plus angle N has to be equal to 90 degrees. This implies that angle N is equal to 90 degrees. This is the reason why we have written that angle N has to be less than 90 degrees. This shows that angle N is less than angle M because angle N is less than 90 degrees but angle M is equal to 90 degrees. So therefore Pm is less than Pn because sides opposite to greater angle is larger. Thus we can say that Pm is less than Pn and hence Pm is the shortest of all line segments from P to 9L right. So this completes the question that was given to us. I hope you enjoyed the session. Do make an appropriate figure whenever you need to prove a given statement to be true. Bye for now.