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# Constructions Class 9 Notes CBSE Maths Chapter 11 (Free PDF Download)

Last updated date: 09th Apr 2024
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## Class 9 Maths Revision Notes for Constructions of Chapter 11 - Free PDF Download

Free PDF download of Class 9 Maths revision notes & short key-notes for Constructions of Chapter 11 to score high marks in exams, prepared by expert mathematics teachers from latest edition of CBSE books.

Also, check CBSE Class 9 Maths revision notes for all chapters:

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## Access Class 9 Mathematics Chapter 11 – Constructions Notes

Introduction:

In geometrical constructions, the process of drawing is done only with the help of an ungraduated ruler known as straight edge and a compass. Sometimes when the measurements are also required, a graduated scale and a protractor may also be used.

Basic constructions:

To construct the bisector of a given angle – Let us have an $\angle ABC$ and bisect it. The steps that needed to be followed are as follows;

1. Draw an arc of any radius, taking $B$ as the centre, that intersects the rays $BA$ and $BC$ at $E$ and $D$ respectively.

1. Now, draw arcs taking $E$ and $D$ as centers taking radius more than $\dfrac{1}{2}DE$ such that they intersect at $F$.

2. Now, draw a ray joining $B$ and $F$ and extending it. Thus, $BF$ is the required angle bisector.

To construct the perpendicular bisector of a given line segment – Let us have a line segment $\overline{AB}$, for which we will draw a perpendicular bisector. The steps to be followed are as follows;

1. Taking $A$ and $B$ as centres, draw arcs on both sides of the line segment with radius more than $\dfrac{1}{2}AB$. The arcs drawn should intersect each other.

2. Let us say that the arcs intersect at points $P$ and $Q$ respectively. Join $P$ and $Q$.

3. Let’s say that the line $\overleftrightarrow{PQ}$ intersects the segment $\overline{AB}$ at point $M$. Then the line $PMQ$ is the required perpendicular bisector.

To construct an angle of ${{60}^{\circ }}$ at the initial point of a given ray – Take a ray $AB$ having initial point $A$ from where we have to draw another ray $AC$ such that $\angle BAC={{60}^{\circ }}$. The steps to be followed are as follows;

1. Take $A$ as centre and draw an arc that cuts the ray $AB$ at some point $D$. Now, taking $A$ and $D$ as centres, and $AD$ as radius, draw two arcs that cut each other, say at point $E$.

2. Join $AE$ and extend it till point $C$ on the ray $AC$. Hence, $\angle CAB={{60}^{\circ }}$.

Some Construction of Triangles:

Measurements of at the least $3$ elements of a triangle are required for the development of a triangle. But all of the combos of $3$ elements aren't enough for the purpose. For example, it isn't viable to assemble a completely unique triangle whilst the measurements of aspects and a perspective that isn't protected in among the given aspects are given. A triangle may be built when (i) the base, one base attitude and the sum of the opposite aspects are given (ii) the base, a base attitude and the distinction among the opposite aspects are given (iii) perimeter and base angles are given.

To construct a triangle, given its base, a base angle and sum of other two sides – Let us suppose, we have to draw $\Delta ABC$, whose base $BC$ and $\angle B$ is given. And the sum $AB+AC$ is also given. The required triangle will be constructed in the steps as follows;

1. First draw the base $BC$ and then make $\angle CBX$ same as the angle given to us at point $B$.

2. Now, mark a point $D$ on the ray $BX$ such that $BD=AB+AC$.

3. Then Join $DC$. Construct $\angle DCY$ such that it is equal to $\angle BDC$.

4. Let us say that the ray $CY$ intersects $BD$ at point $A$. Then $\Delta ABC$ is the required triangle.

To construct a triangle given its base, a base angle and the difference of the other two sides – Let us say, we have to construct $\Delta ABC$, of which the base $BC$, one base angle $\angle B$ and the difference of other two sides either $AB-AC$ or $AC-AB$ are given. This may have two cases as follows;

Case (i): When $AB>AC$

1. First draw the base $BC$ and then make $\angle CBX$ same as the angle given to us at point $B$.

2. Now, mark a point $D$ on the ray $BX$ such that $BD=AB-AC$.

3. Draw the perpendicular bisector of line $CD$, say $PQ$ when extended cut the ray $BX$ at $A$. Hence, $\Delta ABC$ has been constructed.

Case (ii): When $AB<AC$

1. First draw the base $BC$ and then make $\angle CBX$ same as the angle given to us at point $B$.

2. Now, mark a point $D$ on the ray $BX$ extended on opposite side of $BX$ such that $BD=AC-AB$.

3. Draw the perpendicular bisector of line $CD$, say $PQ$ when extended cut the ray $BX$ at $A$. Hence, $\Delta ABC$ has been constructed.

To construct a triangle, given its perimeter and its two base angles – Construct $\Delta ABC$ when the base angles $\angle B$ and $\angle C$ and the perimeter $AB+BC+CA$ are given. The steps need to be followed are as follows;

1. Draw $XY$ that is equal to $AB+BC+CA$.

2. Then make $\angle LXY=\angle B$ and $\angle MYX=\angle C$.

3. Bisect the angles $\angle LXY$ and $\angle MYX$ such that the bisectors meet at point $A$.

1. Now, construct perpendicular bisectors $PQ$ and $RS$ of $AX$ and $AY$ respectively.

2. Suppose $PQ$ intersect $XY$ at $B$ and $RS$ intersect $XY$ at $C$. Then, join $AB$ and $AC$. Hence, we get the required $\Delta ABC$.

## FAQs on Constructions Class 9 Notes CBSE Maths Chapter 11 (Free PDF Download)

1. Which is the best source for Class 9 Maths Chapter 11 exam preparation?

The best resource for CBSE exam preparation are NCERT textbooks. Students must refer to Revision Notes of Class 9 Maths Chapter 11 as it is one of the best study materials which provides them a clear understanding of core fundamentals in an easy and simple manner. Studying these thoroughly before the exams will help the students to improve their problem-solving abilities and to score really well marks. These Revision Notes which are available free of cost on the vedantu website (vedantu.com) will also make the students gain step-by-step understanding of geometry skills. Later, students can practice sample papers and previous year question papers to get a better understanding of exam pattern.

2. How are Revision Notes for Class 9 Maths Chapter 11 helpful for exam preparation?

Revision Notes for Class 9 Maths Chapter 11 are helpful for exam preparation as it provides the students with complete data and knowledge of each concept. They will help the students to face any kind of questions whether it's easy or tough. Practice is the key to success. Students must practice regularly to learn and score high marks in Mathematics. So, Vedantu’s Class 9 Chapter 11 Revision Notes provide students with all the important topics of this chapter. Shortcut techniques, tips and detailed explanations are provided by the Maths experts for practising any concept.

3. What are the important formulas in Class 9 Maths Chapter 11?

In the Revision Notes Class 9 Maths Chapter 11, the important formulas or concepts which are covered are based on the basic constructions and the construction of triangles. All the notes are carefully well structured to make the students gain skills to solve problems. Sample problems along with textbook exercises are provided for the students to get to a clear knowledge of all these concepts in an interesting way. Students must revise each topic thoroughly with the help of these notes. This will for sure help the students to attain proper skills for geometry studies.

4. Why Should I Refer to Class 9 Maths Revision Notes Constructions Chapter 11?

Students should refer to these Revision Notes as they are well-organized and the best learning resources. They are curated by Maths experts of Vedantu to provide the students with a complete and clear understanding of the topics which are covered in the CBSE Class 9 Maths Chapter 11. Going through these notes regularly with full concentration will help the students to gain positive results in Maths exams. These notes will benefit students as it provides them with the right way to approach the Maths exam.

5. Can I download the notes for Class 9 Constructions in PDF?

Yes. Students can download the notes for Class 9 constructions in pdf format for free on the official website of Vedantu (vedantu.com). On the Vedantu website, select study material. Then, under the CBSE section, select CBSE revision notes. Then, select CBSE Class 9 notes. Select the CBSE Class 9 Maths revision notes. Then on the new page select the Chapter 11 Construction revision notes. You can view the notes online or you will get the option to download the pdf. You can also visit the vedantu app to download the PDF.