 Welcome friends again to another theorem and its proof. So in this theorem, it's given that if a line is perpendicular to one of two given parallel lines, then it is perpendicular to other line. Okay, so let's summarize this as given. So given is AB is parallel to PQ and mn is perpendicular to AB. To prove, what is to prove? Prove is mn is also perpendicular to PQ. Okay, so which is you know pretty obvious from the diagram itself. So hence is a angle mcb is equal to 90 degrees. Why? Because mn is parallel to AB. And angle mcb is equal to angle mdq. Why? Because corresponding angles corresponding angles. So that means what? Angle mdq is also equal to 90 degrees. Why? Because mcb was 90 degrees. Hence, hence mn is perpendicular to PQ as well. Hence it is proved. Okay, right. So hence if a line is perpendicular to one of the parallel lines, it will be perpendicular to other parallel lines also. And it is not restricted only to two parallel lines. For example, if you have multiple parallel lines, multiple parallel lines, and let's say there's a transversal. Okay, so let me draw up again. So let's say this is a transversal and let's say any of these angles is 90 degrees. Let's say if it is perpendicular to any one of them, let's say this is l and this is let's say m, this is n and let's say this is P and these are parallel lines. Okay, m and PQ all are parallel lines and any of these angles, let's say this is 90 degrees, then all of them will be 90 degrees. You know why? Because all of them are corresponding angles. So if the line is perpendicular to one line or if this transversal is perpendicular to one of the parallel lines, it will be perpendicular to all the parallel lines. Okay, so that's about the proof.