Mathematics NCERT Grade 9, Chapter 11: Constructions – This chapter starts with a brief introduction on the geometrical instruments and their usage. A geometrical construction is the process of drawing geometrical figure using only two objects which include an ungraduated ruler and a compass,

After a brief introduction, the first section is given which discusses about basic constructions,3 constructions are explained stepwise. These include: 1. To construct the bisector of a given angle,2. To construct the perpendicular bisector of a given line segment.3. To construct an angle of 60 ° at the initial point of a given ray.

Exercise 11.1 contains questions related to basic construction. This is followed by Some Constructions of Triangles, In this section students will learn about the following constructions: 1. To construct a triangle given its base, a base angle, and the sum of the other two sides.2.

To construct a triangle given its base, a base angle and the difference of the other two sides 3. To construct a triangle given its perimeter and its two base angles, Not only the construction but the justification and the reason behind the construction done in a particular way is important. It is not a very long exercise and contains only 5 questions but this chapter needs a lot of practice so that students can attempt all questions of construction in minimum possible time with complete accuracy.

In the examination students should attempt the answers in a stepwise manner. The diagram should be well labelled and neatly drawn. In the end summary of the chapter is provided.

Contents

#### What are the basic constructions covered in Class 9 Maths Chapter 11?

An Overview of CBSE Class 9 Maths Constructions Geometric constructions class 9 walks you through the steps of how different geometrical shapes like triangle, polygons, circle, etc. are drawn with the help of a compass and ruler. The scope of constructions in Maths for class 9 introduces students to the bisection of angles, construction of a perpendicular, etc.

- And is considered vital for solving problems based on geometry.
- You can refer to CBSE class 9 maths constructions solutions to understand the steps of construction and its approach more effectively.
- In turn, it will also help you to solve problems based on Constructions Class 9 NCERT PDF easily.
- Read on to find more about the constructions class 9 CBSE chapter! Constructions Class 9 NCERT – A Brief Overview For geometrical constructions, mostly two instruments are used – a non-graduated ruler and a compass.

Before moving to the concepts covered in the chapter, you need to become familiar with the geometrical tools. You can check class 9 maths constructions NCERT solutions for more details about geometry instruments.A. Components of Geometry Box Typically, a geometry box comprises these important instruments –

A Graduated Scale

This instrument comes in handy for drawing straight lines. One of the sides of the graduated scale is marked in ‘cm’ and ‘mm’, whereas; the other side is marked in inches.

Set Squares

This instrument comprises one set-square with angles 30°, 60° and 90°. On the other hand, the second set comprises angles 45° and 90°. Solve problems on constructions class 9 Maths and find out the use of set squares in practice.

Compass

A compass comes in handy for constructing circles and different angles. It comes with a provision to fit a pencil at the instrument’s end. Refer to solved examples to find out more about how to do construction class 9 with a compass.

Divider

A divider proves useful for measuring lengths accurately. Check out constructions class 9 ex 11.2 to find out if you need to use a divider or not.

Protractor

It is useful in measuring and marking angles accurately. In fact, NCERT solutions of constructions class 9 elaborate the requirement of a protractor for solving constructions class 9 exercise 11.2 and other exercises. With the help of these tools, you will be able to solve construction class 9 extra questions smoothly and will finish exercises like the construction of class 9 exercise 11.1 in no time.B.

Basic Construction for Class 9 CBSE Some of the basic constructions covered in class 9 maths chapter 11 constructions include – i. Construction of an Angle Bisector Step 1 – Take B as the centre and proceed to draw an arc of a specific radius intersecting BC and BA. Name the intersecting points as E and D.

Step 2 – Taking D and E as its centre draw arcs that intersect each other at a point ‘F’ which will make a radius more than ½ of DE. Step 3 – Then, a line BF has to be drawn, which will serve as the required bisector of the angle ABC. Solve the construction of class 9 exercise 11.2 to find similar problems and solved examples.

Ii. Construction of a 60° Angle You may come across problems in construction chapter class 9 exercise 11.1, which will require you to construct a 60° angle. Step 1 – Draw a line QR. Step 2 – Taking Q as the centre, construct an arc with any radius. Mark Y as the intersecting point of QR. Step 3 – Without changing the radius, take point Y as the centre and draw an arc to intersect the previous arc at a point X.

Step 4 – Draw a line QP passing through point X. This will make the required angle PQR. Find a detailed explanation of similar problems in NCERT solutions for class 9 maths chapter 11 study rankers and gain a better understanding of the approach. iii. Construction of Triangles Class 9 ICSE and CBSE (Highlighting the base angle and summation of the two sides of a triangle) Suppose, in a triangle ABC, BC is the base Angle B is the base Summation of the sides (AB+AC) is given.

Step 1 – Draw the base of a triangle BC. Step 2 – Construct angle B to make XBC. Step 3 – A line segment BD has to be drawn, which will make BD = AB+AC on the line BX. Step 4 – DC has to be joined to make the angle DCY = BDC. Step 5 – Intersect BX with CY at point A, making ABC the required triangle. Check out constructions class 9 solutions to learn how to construct triangles and solve problems on them with ease.

You will also find answers to class 9 maths constructions extra questions in the study solutions along with an adequate explanation. iv. Construction of a Triangle when Perimeter and 2 Base Angles are Known Suppose the required triangle is ABC Step 1 – The line segment XY = AB+BC+CA is drawn.

- Step 2 – Make angle MYX = angle C.
- Step 3 – Make angle LYX = angle B.
- Step 4 – Angle LYX and MYX is intersected at a point A.
- Step 5 – PQ will intersect XY at B and RS will intersect XY at C.
- Step 6 – Join AC and AB, making ABC the required Triangle.
- Refer to constructions class 9 NCERT solutions to find step by step explanation about each geometric pattern.

Learn more about the construction of polygons class 9 ICSE and other important shapes under the guidance of subject experts. Join our live online classes and get all your doubts cleared and pick up effective tips to solve NCERT maths exercise 11.1 of class 9 effectively.

#### What are the important topics and subtopics in constructions class 9?

Construction Class 9 Notes – For constructing the angle bisector of angle ABC, take B as a centre construct an arc (any radius) intersecting the rays BA and BC at D and E. Now take E and D as centres and radius more than ½ DE, construct arcs such that they intersect with each other at F. Join BF. This line is the required angle bisector of given angle ABC. Proof: Join EF and DF. Now, from triangle BEF and triangle BDF, BD = BE (Radius of the same arc), DF = EF (Arcs of equal radii) and BF is Common. Therefore, triangle BEF is congruent to triangle BDF by SSS congruence rule. Hence by CPCT, angle EBF is equal to angle DBF.

## What is Class 9 coordinate geometry and Class 9 constriction?

Class 9 Coordinate Geometry – In the class 9 Coordinate Geometry topic you will learn how to identify a point in a space or plane. Learning of a point in space, called it as 3D Geometry whereas the same concepts in-plane is called Coordinate Geometry. Origin : The reference point where distances are marked both in a positive and negative direction. From the figure, 0 represents the origin. Take This Maths Quiz If You Consider Yourself Genius! Cartesian System : The method of fixing a point using vertical and horizontal lines. (i) The above figure illustrates a Cartesian system drawn by combining horizontal and vertical lines. (ii) The X’X horizontal line called the x-axis and YY’ vertical line called the y-axis. (iii) Origin: The point where both X’X and Y’Y intersect each other and is denoted by O. (iv) Now the axes separate the plane into four parts called ” Quadrants “. Vedic Maths Some important pointers of class 9 coordinate geometry and class 9 constriction are-

- If a point lies in the 1st quadrant, then the point will form (+, +) because the 1st quadrant is with the positive x-axis and the positive y-axis.
- If a point lies in the 2nd quadrant, then the point will form (–, +) because the 2nd quadrant is with the negative x-axis and the positive y-axis
- If a point lies in the 3rd quadrant, then the point will form (–, –) because the 3rd quadrant is with the negative x-axis and the negative y-axis
- If a point lies in the 4th quadrant, then the point will form (+, –) because the 4th quadrant is with the positive x-axis and the negative y-axis
- The resulting plane is called a Cartesian plane and the axes are called coordinate axes

Coordinates of a Point From the figure shown above, the point A is obtained after moving 2 units on the x-axis and 3 units on the y-axis.

- The +2 of point A represents X-coordinate and is called abscissa
- From the figure +3 of point A represents Y-coordinate and called as ordinate.
- The coordinates in the brackets show that the x-coordinate comes first, followed by the y-coordinate, Therefore (2, 3) are the coordinates of point A.

### What are constructions in geometry?

What are constructions? – Constructions are accurate drawings of shapes, angles and lines in geometry. To do this we need to use a pencil, a ruler (a straight-edge) and compasses. The basic constructions are perpendicular bisector and angle bisector. In an exam you may have to construct and interpret an angle bisector, a line bisector or distance from a point. Perpendicular bisector Angle bisector Step-by step-guide: Perpendicular bisector Step-by-step guide: Angle bisector Perpendiculars can also be constructed for a point and a given line. Perpendicular from a point to the line Perpendicular with a point on the line Step-by-step guide: Constructions between points and lines Other geometric constructions include how to draw a regular hexagon. Step-by-step guide: How to draw a hexagon The compass constructions can be applied on the same diagram. For example a 60 degree angle can be constructed and used to construct a 30 degree angle. Similarly a 90 degree angle can be constructed and used to construct a 45 degree angle. Step-by-step guide: How to construct a 30, 60, 45, 90 degree angle See also: Constructing triangles