NCERT Solutions for Class 9 Maths Exercise 11.1 Constructions

In lower classes we have drawn certain diagrams to prove certain theorems or for proving a point. These diagrams may not accurate or precise. They provided an aid to solve a question and sometimes for providing proper reasoning.

Now we shall draw accurate diagrams with the help of geometrical instruments like a scale, a compass, a divider, a protractor or sometimes called D. This is one topic in mathematics of class 9 which has practical use in real life.

We can compare the construction in Exercise 11.1 with mechanical drawing which is used by engineers and architects. We will be acquiring the skill to master about 7 or 8 constructions which are really not difficult to master. All these figures are 2 dimensional.

Construction 11.1 relates to construction of the bisector of the given angle. Perhaps this the simplest of construction as per the grade 9 students and we just need a compass and scale for that. Of course, if you have to prove it, we can prove by using SSS rule.

Construction 2 relates to construction of a perpendicular bisector of a given line segment which again is not difficult at all and its proof is also not very difficult.

When we use the term perpendicular bisect it means that the line segment is divided in to two halves which are of equal length and secondly, the bisector is perpendicular (90) to the line segment. Hence, the perpendicular bisector fulfills two properties. It bisects the line segment. It is perpendicular to the line segment.

Examples given just before the exercise 11.1 starts, are important to understand the type of questions given for practice. Construction 3 relates to construction of an angle of 60 from an initial point of a given ray.

Again, this is a very easy construction and its proof barely consists of one or two steps. Exercise 11.1 consists of 5 questions. It is suggested that student practice the construction of 22.5 angle, 75 angle as well 105 angle.