In this unit we are going to study Geometry of Grade VII. In earlier classes we have studied about lines and angles.
If the two lines are drawn in such a way that they do not meet at any point are called parallel lines. Also we conclude that the perpendicular distance between the two lines is equal at all the points. Now if ‘l’ and ‘m’ are any two lines such that l || m. Here if a line ‘n’ is drawn such that it intersect both the lines at a point, then line ‘n’ is called the transversal at parallel lines ‘l’ and ‘m’. Now we observe the following situations to occur if two parallel lines are intersected by a transversal:
a) The pair of corresponding angles is equal.
b) The pair of interior alternate angles is equal.
c) The pair of exterior alternate angles is also equal.
d) The pair of angles on the same sides of the transversal is supplementary. It means that the sum of angles on the same side of the transversal is 180 degrees. (know more about cbse books, here)
Thus we conclude that if any two lines are given and we need to check that they are parallel or not, it means that we need to check any one of the above given conditions are satisfied, then the lines are parallel. So we will try to check that which of the above condition we can show are equal. More over we come across the problems in which we are given that the pair of lines is parallel and there exist a transversal passing through both the lines. Further any one angle among all the angles is given and we need to find the value of all the other angles so formed. We can find all the angles by applying the property of corresponding angles are equal and the interior alternate angles are equal, when the lines are parallel.
In the next session we will discuss about Operations on monomials.
If the two lines are drawn in such a way that they do not meet at any point are called parallel lines. Also we conclude that the perpendicular distance between the two lines is equal at all the points. Now if ‘l’ and ‘m’ are any two lines such that l || m. Here if a line ‘n’ is drawn such that it intersect both the lines at a point, then line ‘n’ is called the transversal at parallel lines ‘l’ and ‘m’. Now we observe the following situations to occur if two parallel lines are intersected by a transversal:
a) The pair of corresponding angles is equal.
b) The pair of interior alternate angles is equal.
c) The pair of exterior alternate angles is also equal.
d) The pair of angles on the same sides of the transversal is supplementary. It means that the sum of angles on the same side of the transversal is 180 degrees. (know more about cbse books, here)
Thus we conclude that if any two lines are given and we need to check that they are parallel or not, it means that we need to check any one of the above given conditions are satisfied, then the lines are parallel. So we will try to check that which of the above condition we can show are equal. More over we come across the problems in which we are given that the pair of lines is parallel and there exist a transversal passing through both the lines. Further any one angle among all the angles is given and we need to find the value of all the other angles so formed. We can find all the angles by applying the property of corresponding angles are equal and the interior alternate angles are equal, when the lines are parallel.
In the next session we will discuss about Operations on monomials.
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