Constructions Class 10 Notes CBSE Maths Chapter 11 (Free PDF Download)

Division of a Line Segment:

Follow the given below steps to divide a line segment internally in a given ratio \[\text{m:n}\], where both \[\text{m}\] and \[\text{n}\] are positive integers. 

Step 1: Draw a line segment \[\text{AB}\] of a given length using a ruler.  

Step 2: Draw any ray \[\text{AX}\] making an acute angle with \[\text{AB}\].  

Step 3: Along \[\text{AX}\] mark off \[\left( m+n \right)\] points, namely \[{{\text{A}}_{1}},{{A}_{2}},....,{{A}_{m}},{{A}_{m+1}},...{{A}_{m+n}}\]

Step 4: Join \[B\] to \[{{A}_{m+n}}\]

Step 5: Through the point \[{{A}_{m}}\] draw a line parallel to \[{{A}_{m+n}}B\] at \[{{A}_{m}}\]. Let this line meet \[\text{AB}\] at '\[\text{C}\]'   which divides \[\text{AB}\] internally in the ratio \[\text{m:n}\]. 

Proof: 

In \[\vartriangle \text{AB}{{\text{A}}_{m+n}}\], \[C{{A}_{m}}\] is parallel to \[\text{B}{{\text{A}}_{m+n}}\].  

By basic proportionality theorem, we get,        

Here '\[\text{C}\]' divides \[\text{AB}\] internally in the ratio \[\text{m:n}\]. 

To Construct a Triangle Similar To a Given Triangle as Per the Given Scale Factor:

Construct a \[\vartriangle \text{ABC}\] in which\[BC=4cm\], \[\angle B={{60}^{0}}\] and \[\angle C={{45}^{0}}\]. Also, construct a triangle whose sides are \[\frac{4}{3}\] times the corresponding sides of \[\vartriangle \text{ABC}\].  

Steps of Construction:  

Step 1: Construct a triangle \[ABC\] with the given data that are \[BC=4cm\], \[\angle B={{60}^{0}}\] and \[\angle C={{45}^{0}}\] 

Step 2: Now construct an acute angle \[CBX\] downwards.  

Step 3: On \[BX\], make four equal parts and mark them as \[{{\text{B}}_{\text{1}}}\text{, }{{\text{B}}_{\text{2}}}\text{, }{{\text{B}}_{\text{3}}}\text{, }{{\text{B}}_{\text{4}}}\].  

Step 4: Join '\[\text{C}\]' to \[{{\text{B}}_{\text{3}}}\] and draw a line through B4 parallel to \[{{\text{B}}_{\text{3}}}C\], intersecting the extended line segment \[\text{BC}\] at \[\text{C }\!\!'\!\!\text{ }\].  

Step 5: In the same way draw \[\text{C }\!\!'\!\!\text{ A }\!\!'\!\!\text{ }\] parallel to \[\text{CA}\]. Thus \[\vartriangle \text{A }\!\!'\!\!\text{ BC }\!\!'\!\!\text{ }\] is the required triangle similar to \[\vartriangle \text{ABC}\] whose sides are \[\frac{4}{3}\] times the corresponding sides of \[\vartriangle \text{ABC}\]. 

Construction of Tangents to a Circle:

Given below are the steps to construct the tangents to a circle from a point outside it  

Given: A circle with center '\[O\]' and a point ' \[P\] ' outside it  

Required:  Construct the tangents to the circle from \[P\].  

Steps of construction:  

Step 1: First Draw a circle with center '\[O\]'  

Step 2: Join \[OP\].  

Step 3: Draw the perpendicular bisector \[OP\]. It meets \[OP\] at '\[M\]'.  

Step 4: Taking '\[M\]' as center and \[OM\] as radius draw arcs which cut the circle with center '\[O\]' at two points. Name them as \[Q\] and \[R\].  

Step 5: Join \[PQ\] and \[PR\].

Step 6: \[PQ\] and \[PR\] are the required tangents to the circle with center '\[O\]' from an external point '\[P\]'.  

Note:  We can prove that the length of \[PQ\] and \[PR\] are equal

Constructions Class 10 Notes PDF

On the official website and mobile app of Vedantu, the Class 10 notes for the construction chapter are available in a PDF version that is for free to download. These PDF files are very helpful for students, which helps them use these study materials to understand their learning. The physical copy can be stored and utilized for future purposes. As the material is prepared by well-experienced faculty, the language used to explain is very simple and straightforward. It also provides various simple techniques to understand the concept and solve it quickly for competitive exams.

Constructions Note Class 10

The constructions chapter prepared by the experienced faculty consists of all the four topics covered in the textbook. Namely:

11.1 Introduction:-

Some basic concepts and the definitions of the construction chapter were explained in class 9, and it should be given a quick recap in the introduction of the construction chapter of Class 10. Because the 10th class subject is somehow advanced than class 9, students need to understand the basics of construction to proceed further in class 10.

11.2 Division of a Line Segment

In this section, the PDF prepared by the faculty available on the official website of Vedantu has explained the division of line segments. The line segment May divide in a proportional ratio, and it can be proved by Thales theorem, which is also known as the basic proportionality theorem. Students need to learn and understand the fundamentals of the theorem to achieve the knowledge of explaining it to others.

11.3 Construction of Tangents to a Circle

The next section of the constructions of Class 10 is about constructing a tangent to the circle. While constructing the tangent to the circle, we need a point from the outside. Also, we have two possibilities while constructing a tangent to the circle. One is if the point considered to draw the tangent is lying on the circle. And the other case is the point lies outside the circle to draw a tangent.

Constructions Class 10 example 1 is to construct tangents to a circle from a given point outside it. That means it is the second case of constructing a tangent. The print doesn't lie on the circle.

Let us consider C will be the given circle with center O and a point P outside it. We have to draw tangents to the circle from the point P. 

For constructing the tangents, we need to follow a set of sequential steps as follows -

1. Join PO and bisect it. Let M be the midpoint of PO.

2. Keeping them as the midpoint, join PO, and draw a bisector to it.

3. Then draw a circle by taking M as center and MO as radius, Let it intersect the given circle at the points Q and R.

4. Now join PQ and PR as tangents. Hence we can draw two tangents using the point which lies outside of the circle.

If we need to construct a tangent from the point lying on the circle, it is simple and straightforward. We can construct tangents using the radius directly.

11.4 Summary

The Class 10 constructions chapter has the last section, summary. In this section, all the concepts have been given, and revision exercises are also provided for students. The entire notes given further chapter can be given as a quick recap of highlighted points. During the examination time, students can glance at this summary and memorize all the concepts available in the chapter. So somebody and revision exercises are very important for the whole chapter.

Constructions is one of the chapters in CBSE Class 10 Maths where students must pay close attention to details and data available in the questions. To make things easier, our expert teachers have come up with study materials that students can consume easily to be able to use for improving their understanding of the topic without much complication. Our advice to students is that they read through these notes as well as check out the other related links given in this article to derive the best possible outcome.

Benefits of CBSE Class 10 Chapter 11 Constructions Notes

• The notes prioritize main topics for focused studying, aiming to provide convenient and comprehensive material for a thorough understanding of concepts.

• Simplified descriptions of construction methods facilitate quicker comprehension, allowing for efficient practice and skill mastery.

• With these precise notes on geometric figure construction, resolving doubts becomes hassle-free. Quick reference to the notes aids in clarifying uncertainties promptly.

• For an efficient chapter preparation, use these notes to optimize study time and ensure a thorough grasp of the subject matter.

Download the CBSE Class 10 Maths Constructions PDF

Get the free PDF version of these notes and download it to your computer. Access these notes whenever you want and prepare the chapter easily. Find out how simple the experts have explained the process and follow the method. It will help you to formulate precise answers to the questions asked in the exercises and in the exams.

CBSE Class 10 Revision Notes - Other Chapters

The following is a list of links that take you to the revision notes for every chapter included in the CBSE Class 10 syllabus. We advise students to check these links out to make the best use of Vedantu’s study materials for Class 10 exams. 

• Chapter 1 - Real Numbers Revision Notes

• Chapter 2 - Polynomials Revision Notes

• Chapter 3 - Pair of Linear Equations in Two Variables Revision Notes

• Chapter 4 - Quadratic Equations Revision Notes

• Chapter 5 - Arithmetic Progressions Revision Notes

• Chapter 6 - Triangles Revision Notes

• Chapter 7 - Coordinate Geometry Revision Notes

• Chapter 8 - Introduction to Trigonometry Revision Notes

• Chapter 9 - Some Applications of Trigonometry Revision Notes

• Chapter 10 - Circles Revision Notes

• Chapter 12 - Areas Related to Circles Revision Notes

• Chapter 13 - Surface Areas and Volumes Revision Notes

• Chapter 14 - Statistics Revision Notes

• Chapter 15 - Probability Revision Notes

Conclusion

For an enhanced comprehension of this subject, NCERT - Class 10 Maths Chapter 11 - Constructions thoughtfully prepared by experienced educators at Vedantu is your invaluable companion. These notes break down the complexities of “Constructions” into easily digestible sections, helping you grasp new concepts, master formulas, and navigate through questions effortlessly quickly in the last minute as well. By immersing yourself in these notes, you not only prepare for your studies more efficiently but also develop a profound understanding of the subject matter.