 Hello and welcome to the session. In this session we will discuss the definition of basic concepts used in geometry like line segment, angle, circle, parallel and perpendicular lines, using motion of line, point, distance along a line and distance around circular arc. First of all let us discuss what is a point? Now a point is an undefined term, a point is a specific place in space and it has no length width. Now a point is represented by placing a dot on a paper and it is labeled by a single capital letter. Now here we can represent this point by capital letter A. Now we use a point to mark a location or position. Now suppose we have to represent the vertices of a triangle ABC. Now these vertices can be represented by point AB and discuss what is a line. Now a line is a set of continuous points that extend indefinitely in either direction. Now the term line will mean a straight line. We know that a line is a set of continuous points that extend indefinitely in either direction. It means a line extends indefinitely in both directions. It does not have endpoints and here arrows on both the sides that this line extends indefinitely in both directions. There are in on this line. So what is a line? Now we know that this is a line. Now let us take NP on this line. Now on this line the part AB is the line segment joining the two points A and B. AB is a line segment A and B are a pair of this line segment AB. So line segment is a part of the straight line with two fixed endpoints. Now let us discuss in a plane which are always at a fixed never meet this diagram showing parallel lines L1 and L2. These arrow heads are used and you can also see that there is a fixed distance between these two lines. We write parallel lines never intersect or meet at any point. Now let us discuss what is an angle? Whenever two lines or edges meet an angle is formed. Now an angle is formed by two arms vertex. Angle be represented by theta. So here you can see that we have two arms which meet at vertex and the theta is formed by the arms. Now angles can be right acute. Now if the two lines meet at 90 degrees or intersect at 90 degrees then the lines are perpendicular. In this diagram you can see that the lines L1 and L2 intersect each other at the point O making an angle of 90 degrees. So the lines are perpendicular to each other and we write that L1 is perpendicular. Now perpendicular lines intersect at a point making a right angle. Now let us discuss what is a circle? A circle is a plane figure whose boundary that is circumference consists of points. Now here this is the circle radius. Now a line is neither of points that has no thickness or width and goes on forever. Now a line is not measurable because there is a distance between any two points on a line. That is we can find length of line segment which can give us the distance between two points on line. Now in a coordinate plane let X1 variable in plane given by AB and here we get a line segment AB. Now we have to find distance between these two points or length of line segment AB. Now distance between the points A and B is given by X1 whole square plus Y2 minus Y1 whole square. And this is called the distance formula between any two points or length is always positive. Be the midpoint of line segment AB. Now midpoint is the point which divides the given line segment into two equal segments. Here C divides the line segment AB into two equal segments AC and CB. Now we can find the coordinates of the midpoint formula, coordinates of CR, X1 plus AC is Y1 plus Y2. Now suppose we have a point A with coordinates minus 1, 2 and point B with coordinates of the line segment AB of A by X1 Y1 and coordinates of B by X2 Y2 B is equal to square is 1 whole square is Y1 whole square. Now putting the values of X1 Y1 X2 Y2 in this formula it is equal to square root of L is 1, 2 whole square of minus 1 is 5 plus 1 which is 6 and here it will be 6 square plus now 4 minus 2 is 2 so this will be 2 square is 36. So this is equal to square root of which is equal to square root and this is equal to 2 square into 10 which can be written as square length of line segment AB is equal to of this line segment AB. Now coordinate and Y1 plus Y2 square upon 2 minus 1 is 4 and 4 upon 2 is 6 and 6 upon 2 is 3 so coordinates of midpoint B is rotated at a particular angle may be 90 degrees or 45 degrees or 180 degrees etc. In clockwise a circular path using the distance formula we can find the path described by a point when the point is rotated at a particular angle. Now suppose the fixed coordinates 00 and the moving point B now using distance formula let us find the distance OP is equal to square root of X2 minus X1 whole square plus Y2 minus Y1 whole square OP is equal to R the values of X1 Y1 and X2 Y2 X minus 0 whole square plus Y minus 0 whole square this gives R is equal to X2 plus Y2 is equal to R square of circle with center having coordinates 00 that this is the equation of a circular path we can have as center circular path using the distance formula equation of circular path will be is equal to R square. So in this section we have learnt definition of circle, angle, lines and perpendicular lines using notion of point line have enjoyed the session.