 Hi and welcome to the session. Today we will learn about pairs of lines. First of all we have intersecting lines, intersect if they have a point in common. Like this, now here the common point say O is called the point of intersection of the two lines L and M. Now you will find that two lines cannot intersect in more than one point. Next we have transversal a line that intersects two or more lines at distinct points transversal line P intersects two lines L and M at distinct points. So here line P is a transversal to the lines L and line P intersects lines L and M at same point. So that means here line P is not a transversal to the lines L and M because line P does not intersects lines L and M at distinct points. Our next topic is angles made by a transversal. Lines L and M are cut by the transversal P and in this we have marked the eight angles formed by the lines L and M with the transversal P. Here the angles marked from 1 to 8 have their special names. So let's see that angle 3, angle 4, angle 6 are called interior angles, angle 1, angle 2, angle 7 and angle 8 are called exterior angles. Next we have angle 1 and angle 5, angle 7, angle 4 and angle 8 corresponding angles. Now let us consider one pair of corresponding angles say angle 1 and angle 5. The corresponding angles have different vertices they are on the same side of the transversal like here angle 1 and angle 5 are on the same side of the transversal. And they are in corresponding positions like above or below left or right relative to the two lines. And angle 6, angle 4 and angle 5 alternate say angle 3 and angle 6 have different vertices they are on the opposite side of the transversal. Like angle 3 is on the left of the transversal and angle 6 is on the right of the transversal and they lie between the two lines that is L and M. Now angle 1 and angle 8 and angle 2 and angle 7 form pairs of alternate. And lastly we have angle 3 and angle 5 and angle 4 and angle 6 interior on the same side. Let's move on to our next topic transversal of parallel lines. First of all let us see what are parallel lines. When drawn on a sheet of paper do not meet however far produced we call them to be parallel lines. So here line N and line M do not meet anywhere. So that means line N and N are parallel lines. Transversal P cuts at distinct points. Now when a transversal responding angles are equal so here angle 1 is equal to angle 5. Angle 3 is equal to angle 7. Angle 2 is equal to angle 6. Angle 4 is equal to angle 8. Next we have alternate interior angles equal. So this implies angle 3 is equal to angle 6. Angle 4 is equal to angle 5. Lastly of interior angles transversal supplementary. That means angle 3 plus angle 5 is equal to 180 degrees that is their supplementary. Also angle 4 plus angle 6 is equal to 180 degrees. Now our last topic is checking for parallel lines. Here we have 3 rules when a transversal corresponding angles are equal. Lines have to be second alternate. Interior angles are equal then line. Interior angles on the of the transversal supplementary then lines have to be parallel. Now let's take an example. Line N and M are cut by the transversal N and we have given the measure of these 2 angles and we need to check whether line N is parallel to line M or not. So first of all let us mark all the angles over here. Now here we have given that angle 4 is equal to 136 degrees and angle 6 is equal to 44 degrees. If we add angle 4 and angle 6 then we will get angle 4 plus angle 6 is equal to 136 degrees plus 44 degrees which is equal to 180 degrees. Now angle 4 and angle 6 form a pair of interior angles on the same side of the transversal and they are supplementary also and we know that when a transversal cuts 2 lines such that a pair of interior angles on the same side of the transversal is supplementary then the lines have to be parallel. So that means line N is parallel to line M. With this we finished this session. Hope you must have understood all the concepts. Goodbye, take care and have a nice day.