Solving the mystery lying within a Parallelogram

One of the most interesting topics is Geometry, which is indeed an area to score more marks is that of the parallelograms.  The study of this geometric figure is very interesting as it covers diverse aspects like the relationship between the opposite angles and sides, diagonals, adjacent angles, as well as the angles, generated by the diagonals.

It is for sure, you will start finding more interest to understand and master the problems themed on this topic, and it will certainly enable you to acquire more expertise in geometry, which is one of the best areas to score more and more marks on the maths paper.

The basic rules for the angles and sides in a Parallelogram

To explain a Parallelogram in the simplest terms, it is basically a quadrilateral that comes with double pairs of  parallel lines. To get into the basic rules in this regard, you need to remember that, the opposite sides of this figure will always feature equal length and would lie in parallel to each other. Inside, the angles at the opposite sides will always be congruent angles and the ones, lying next to each  other will be always supplementary angles.

The diagonals in this figure will always serve the purpose of bisecting each other, and once,  a diagonal is drawn, it is going to create multiple angles that will comply with a basic rule, just like the angles formed through the intersection of 2 parallel lines by any transverse.

Further, you should keep in mind that the alternate interior angles should be always equal, just as the vertical angles. The interior angles at the same sides are always equal to each other. Remembering these basic rules in very important, as you will inevitably need it, each time you need to solve a problem based on this figure.

An overview of the technique to solve problems based on parallelograms

Assume a parallelogram with sides ABCD. The reason to give  such a name to this figure is that, it involves 4 parallel lines.  Here, the sides BC and AB are parallel to the sides AD and CD. These pairs of sides are not only parallel to each other, but holds a congruent relationship between them. Also to state that, the angles across each other, share a congruent relationship.

The alternative approach to pair the angles would be based on supplementary relationship. The summation of the angles that lies next to each other, alternatively known as adjacent angles, should be 180 degrees.

Now assume that diagonals are drawn between the points A to C and B to D. As diagonals basically bisect each other, the diagonal BD will split the side AC by half, and same will be the  impact of the diagonal AC that will divide the side BD to its half. As a plethora of parallel lines are going to be intersected  by a transverse, it will ultimately form interior angles.

A detailed understanding of this explanation will enable you to master the concept related to this figure and easily solve the problems related to it.

How to develop the bets competency in solving these problems?

Now, assume, you are facing lots of issues in understanding and working on this figure. How will you overcome such challenges? Is there any simple way that will enable you to master the concept and effectively solve all the problems related to this geometric figure? Here come some simple tricks and tips that will be worthy to follow:

  • Turning away from the problem will not help: if you are unable to understand the properties and the features of a parallelogram, it is  likely that you will grow reluctant to work on such problems. But, should you do that, you are going to commit the biggest blunder. Running away from the problems will not help. Rather, you are suggested to work more on such problems that will enable you to handle such problem better. Remember, practice is the only way to attain perfection and it holds high relevance when it comes to the domain of mathematics. So, the more difficulty you are facing, you should devote more and more time in practicing these problems that will enable you to master the tricks after you practice for a certain span of time.
  • Try to learn alternative methods of solving these problems: as true for any other lesson from mathematics, there should be several ways to solve these problems. So, if you are unable to understand one specific way, you should not lose your heart. Rather, you should try to learn alternative approaches to solve these problems, complying with the basic rules and regulations. Even if you are facing hardship to understand one specific method, it can be that, you would be able to master the alternative ways easily. This will be only possible, when you give the concept some good extent of though and you try to understand the concept, rather than simply mugging it up.
  • Don’t panic: do you know, when you will find it the most difficult to learn new things? It will happen in the instances, when you will start to panic. So, even if you are finding it tough to master the rules and concepts, you should not panic for it. Rather ,you should allow ample time to learn the things by heart and go about practicing that will make you confident about handling these problems. This is a simple trick that will never fail.
  • There is no harm in asking your teacher for the second or the subsequent times: it is obvious that, the first time you will learn this lesson, some confusions will inevitably come up in your mind. You should not feel shy to ask your teacher for the second or the subsequent times, should such confusions and doubts to come up. It is certainly a much better approach than pretending to have learnt the concept, while you still have doubts and confusions about it. Pretention to have understand the concepts related to the parallelogram will surely not going to go well.