Geometry

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. 

Multistep problems

In this unit we are going to learn how to solve multistep problems. This unit is designed for Grade VII.  When we have certain equations, which are having one variable, we proceed in the way that in every step, we move towards separating all constant values from the variables. This can be done in single steps, when the equations are small. But in the bigger equations which include multi operators existing in the equation, can be solved step by step. In the initial step, we will first shift all the variables to one side of the equation. While shifting we must remember that the positive term changes to a negative term and the negative term changes to a positive term. Here we can do the same process in another way, if the term which is negative on the right side of the equation has to be shifted to the right side of the equation, and then we simply add positive value of the same term on the both side of the equation. Thus the positive and the negative term of the right side of the equation will be cancelled, on another hand the positive of the same value will be added to another side of the equation.

We can proceed in the same method for subtraction too. Thus any negative value from one side of the equation is to be removed, for this we will add the same value on the both sides of the equation. This becomes possible as the addition and the subtraction are inverse of each other.

 Now we look at multiplication and division sign which appears in the equation. To separate the variable, we need to see that the constant value with the variable consists of the multiplication operator or the division operator. If the operator is of multiplication, divide both sides of the equation by the same number and if the operator is of division, multiply both sides of the equation by that number. It will give the resultant value of the variable.

In the next session we are going to discuss Geometry.