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# RD Sharma Class 10 Chapter 11 Solutions (Constructions)

Our RD Sharma Class 10 Maths Solutions Chapter 11 – Constructions are the best study material to prepare well for the CBSE Board exams. This chapter is a part of Geometry, which teaches you to construct Geometrical shapes along with complete reasoning behind working of such constructions. Here you will learn how to divide a line segment, how to construct a triangle which is similar to a triangle given already according to the given scale factor, and how to construct the tangents to a circle from a point outside it in different steps.

There are 3 exercises containing a total of 19 questions in this chapter of RD Sharma Class 10 Maths Solutions Book. Our talented team of mathematicians have framed the solutions to help you learn easily and effectively. All the questions have been answered thoroughly describing all steps of construction required. After solving these questions, you learn how to divide a line segment in a particular ratio and also justify the construction done. You will also learn how to draw angles and then bisect the angles into two angles of different measures. This chapter also teaches you how to draw linear and vertically opposite pair of angles and bisect them. You will also learn how to draw angles of different measures using only a ruler and a compass. You shall also be taught how to justify the constructions done in a step by step manner.

The solutions of RD Sharma Class 10 Maths Constructions are framed in such a way that they make the learning process engaging, interactive and efficient. They include all the concepts of this chapter and gives you complete knowledge.

## RD Sharma Class 10 Maths Constructions: Important Topics

Class 10 Maths Constructions deals with the construction of geometrical figures by using different geometrical tools and also teaches you how to give the mathematical reasoning behind the methods of constructions. The concepts taught in the chapter are discussed below.

• Division of a Line Segment

This part of the chapter teaches you the steps of the method for dividing a line segment in a given ratio, without a measuring tool. The line segment is converted into an acute angle before performing other steps with the help of compass and ruler. There is an alternative method which uses the idea of drawing a similar triangle as a given triangle where sides of both the triangles (new and old) are in a given ratio.

Here you will also learn how to construct a triangle similar to a given triangle as per given scale factor where scale factor means the ratio of the sides of the new triangle with the corresponding sides of the given triangle. So, the newly constructed triangle may be smaller or larger than the given triangle, i.e. the scale factor may be less than 1 or greater than 1.

• Construction of Tangents to a Circle

You learn in this part of the chapter that a required tangent can be drawn simply by first drawing the radius through the chosen point and then drawing a line perpendicular to this radius through the chosen point.

You will also learn that from a point given outside the circle, there can be two tangents to the circle. Here you learn how to construct two tangents to a circle from a point outside the circle and then justify the construction. The method needs knowledge of the centre of the circle. In case the centre is not given, you need to locate its centre first by taking any two non-parallel chords and then finding the point of crossing off their perpendicular bisectors.

For all the constructions covered in this chapter, the steps of construction have been laid out in details and follow a logical flow to help you learn well.

### RD Sharma Class 10 Maths Chapter 11 Exercises

All the 3 exercises given in the chapter are meant to give you ample practice of the concepts learnt here. Our solutions of RD Sharma Solutions for Class 10 Maths Chapter 11 exercises have been written in a step by step manner so that you can get a good hold of the process and utilize the same for answering class 10 board exam questions efficiently. The detailed components of the exercises are given below.

Exercise 11.1

There is a total of 3 questions in this exercise. Question 1 asks you to determine the point on a line segment which divides it in a 2:3 ratio. Questions 2 and 3 ask you to divide a line in the given ratio and also provide justification for the construction done.

Exercise 11.2

This exercise consists of 10 questions. Question 1 asks you to first draw an angle and then construct another equal angle. Question 2 asks you to bisect the given angle and measure the resultant angles. Question 3 and 4 ask you to draw an angle by using the protractor and then construct an angle which is half of the previous one.

Question 5 asks you to draw a linear pair of angles and then bisect the two angles. Question 6 asks you to draw a vertically opposite pair of angles and then bisect the two angles. Questions 7 and 8 asks you to draw angles of different measures using a ruler and a compass only. Question 9 asks you to draw an angle and then bisect it into two angles of different measures. Question 10 asks you to construct an angle at the initial point of a given ray and also justify the construction.

Exercise 11.3

There are 6 questions in this exercise. Questions 1 to 4 asks you to draw a circle of the given radius and then construct a pair of tangents from a given point(s) outside the circle. Question 5 asks you to draw a pair of tangents, on a circle of the given radius, inclined to each other at a given angle. Question 6 asks you to construct a triangle and then a circle around it with specific instruction and finally a tangent to the circle.

### Benefits of RD Sharma Class 10 Maths Solutions for Chapter 11 – Constructions

• They help you build a strong conceptual foundation of the concepts taught in the chapter.
• These solutions give you tips and techniques to remember and correctly apply the concepts in your Class 10 Board exams and in your higher classes.
• They are a handy source of study to learn and revise all the topics mentioned in this chapter during board exams.
• They give you a fair idea regarding the types of questions asked in your board exams and the best ways to solve the same.