 # Constructions

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 –

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.

To gain a better idea about construction chapter class 9, download our class 9 maths exercise 11.2 solutions and develop an effective approach towards the chapter and its exercises.

1. What is the Basic Difference Between a Ruler and Straight Edge?

Ans. The basic difference between the two instruments is that a straight hedge is mostly used to draw a straight line, but it is not usually used to measure a length. Resultantly, it does not comprise any measurement gradient. Contrarily, a ruler is used for both purposes and has cm marked on one of its sides and inches on the other. Rulers are probably one of the most commonly used and most recognisable instrument.

2. What is the Application of Geometry in Real Life?

Ans. When looked at closely, geometry has found wide application in our daily life. For example, geometry is useful in calculating volume, area and circumference of objects. Also, the geometric shapes are extensively used in our everyday lives and beyond that. For instance, it has found wide application in the field of sports, video game, quilting, food design, etc. It is an application based science which have become an integral part of modern life.

3. How to Define a Perpendicular Bisector of a Triangle?

Ans. A perpendicular bisector of any triangle can be a line which is perpendicular to its side and passes through the midpoint. Circumcentre is a vital point in a triangle; it is where all 3 perpendicular bisectors of the triangle meet. Notably, the circumcentre is equidistant from the triangle’s vertices.

4. What is the Median? Can a Perpendicular Bisector Serve as a Triangle’s Meridian?

Ans. Median is a line segment extending from a triangle’s vertex reaching to the midpoint on vertex’s opposite side. A perpendicular bisector can serve as a triangle’s meridian. To elaborate, when median meets the opposite side at 90°, it becomes a perpendicular bisector of that particular side. For instance, in case of an equilateral triangle, all medians are perpendicular bisectors. Similar examples can be found in other geometrical shapes as well.