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# RD Sharma Class 9 Chapter 17 Solutions (Constructions)

In RD Sharma solutions for class 9 chapter 17, you will learn some basic constructions with the help of ruler and compasses. Construction of bisectors, standard angles, triangles and measurement of length is some basic study of the chapter.

Chapter of RD Sharma Solutions 17 consists of 3 exercises with 28 practical questions. The questions involve drawing, bisecting and measuring the line segment of particular length or angle. Additionally, you will come across the question of constructing some standard angles and measuring the angles later. There is also the construction of triangles in the presence of some conditions.

Instasolv has prepared the solutions for you so that you can learn the basics of constructions. This will help you in future to solve complex construction related questions. Foundation of any topic is the strength to achieve mastery later. The chapter does not only hold its importance in your books but also in real life. For instance, you will need the help of constructions in determining circumference, area, volume. It is used in various fields like Sports, Technology, Architecture, Designing and many more. Therefore, Instasolv has taken a step to make your base strong in relationship with chapter constructions.

## Topics covered in RD Sharma Solutions for Class 9 Chapter 17

Bisector of a Line Segment

When we bisect any line segment, that means we are dividing the line into half equal parts. Although, plotting the centre of any line is easy with the help of a ruler but its authenticity is a sceptic. Therefore, there is a rule with a step by step process to bisect a line segment.

Steps of construction are:

1. Make a line of a given length. Suppose it by the name of line PQ.
2. With centre P and radius more than half of PQ, draw an arc on each side of PQ.
3. Repeat the previous step but now with centre Q.
4. This will cut both the arcs. Now join the points. The point where it touches PQ, that point is the bisector of the line segment.

## Bisector of an Angle

Bisecting an angle is a task to divide the angle into equal parts. It involves drawing a ray on the inside of an angle in such a way that it divides the whole angle into half.

Steps of construction-

1. Create a given measure of the angle. Suppose angle QPR, P being the centre.
2. From P, draw an arc cutting PQ and PR. Let’s call them R and S
3. Draw an arc from R and S respectively with radius more than half.
4. Produce it as T. then join PT.

### Construction of an Angle of 60°

For constructing a 60°angle, you will need the help of a ruler and compass.

Steps of Construction-

1. Draw a ray AB. With centre A, draw an arc of any radius and cut the ray AB at P.
2. With the same radius draw another arc from centre P by cutting the arc and producing Q.
3. Join AQ.

### Construction of an Equilateral Triangle

As we all know, the equilateral triangle is a triangle which has it’s all sides equal. Its internal angle is 60°. For the construction of the equilateral triangle also, there is a step by step procedure.

Steps of construction-

1. Draw a ray PY, P being centre.
2. With centre P, draw an arc with the radius similar to the length of the side, cutting PY at R.
3. With centre R, draw an arc with the same radius, cutting the arc at Q.
4. Join PQ and RQ to get your required triangle PQR being equilateral.

There are different constructions of a triangle for each given condition. They are-

• When its base, the sum of the other two sides and one base angle are given.
• When its base, difference of the other two sides and one base angle are given.
• When parameter and two base angles are given.

## Discussions of RD Sharma Solutions for Class 9 Chapter 17

1. In exercise 17.1, you will see all the questions related to drawing bisectors, measuring bisectors and obtaining a line segment of a given length.
2. A couple of questions also demand drawing a perpendicular bisector.
3. Exercise 17.2 is all about the construction of different types of angles like a right angle, linear pair angle and angle with given measures.
4. The question bank is full of constructing angles and bisecting it.
5. At some point, you are asked to verify and justify your Construction.
6. Exercise 17.3 involves justifying your construction of the triangle according to the given condition.
7. Based on the given parameter and data, you will have to construct a triangle which includes all the conditions.

## Benefits of RD Sharma for Class 9 Chapter 17 by InstaSolv

1. As the constructions are all about perfection and minute measurement, InstaSolv has prepared its best to help you understand the concept of a chapter of RD Sharma Class 9 Maths Solutions with ease.
2. Constructions are what you can utilize in your real life. So, studying it in a practical way would be helpful for you in the future.
3. InstaSolv has a solution where you will only find the easiest steps to learn.
4. Brainstorming is great but saves it for later. For now, we are here to support you in every doubt which comes up in your mind.
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