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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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FAQs on Constructions
1. What are geometric constructions in Class 9 Maths?
In Class 9 Maths, as per the CBSE 2025-26 syllabus, geometric constructions refer to the process of drawing accurate geometric figures, such as lines, angles, and triangles, using only two specific tools: an ungraduated ruler (a straightedge) and a compass. The focus is on the logical, step-by-step process and the geometric principles that justify each step, rather than on measurement.
2. What is the difference between a ruler and a straightedge in geometric constructions?
The key difference lies in their function. A straightedge is used simply to draw a straight line or connect two points; it has no markings for measurement. A ruler, on the other hand, has markings (like centimetres or inches) and can be used for both drawing straight lines and measuring their length. In pure geometric constructions, we use a straightedge.
3. How do you construct the bisector of a given angle using a compass?
To construct an angle bisector, you follow these steps:
- Place the compass point on the vertex of the angle and draw an arc that intersects both arms of the angle.
- From these two intersection points, draw two more arcs of the same radius in the interior of the angle, ensuring they cross each other.
- Use a straightedge to draw a line from the vertex to the point where these two new arcs intersect. This line is the angle bisector.
4. What are the steps to construct the perpendicular bisector of a line segment?
The construction of a perpendicular bisector for a line segment AB involves these steps:
- Open the compass to a radius that is more than half the length of the line segment AB.
- With A as the centre, draw an arc on both sides of the line segment.
- Keeping the same compass radius, now use B as the centre and draw two more arcs that intersect the first two arcs.
- Join the two intersection points of the arcs using a straightedge. This line is the perpendicular bisector of AB.
5. Why are only an ungraduated ruler (straightedge) and a compass used for 'pure' geometric constructions?
Using only a straightedge and a compass is a classical tradition dating back to ancient Greek mathematics. The limitation is intentional and serves a crucial purpose: it forces the focus on the logical reasoning and geometric theorems that underpin the construction. Every step must be justifiable using geometric axioms and postulates, making it an exercise in logic rather than simple measurement. This method ensures that the constructed figures are theoretically perfect, independent of the accuracy of a measuring scale.
6. What is the difference between an angle bisector and a perpendicular bisector in a triangle?
While both are important lines within a triangle, they have different definitions and properties.
- An angle bisector is a line that divides an angle of the triangle into two equal angles. It starts from a vertex and ends on the opposite side.
- A perpendicular bisector is a line that is perpendicular to a side of the triangle and passes through that side's midpoint. It does not necessarily have to start from a vertex.
7. How do you construct a triangle when its base, a base angle, and the sum of the other two sides are given?
According to the NCERT Class 9 syllabus, the construction involves these key steps:
- Draw the base segment and construct the given base angle at one endpoint.
- From the vertex of this angle, cut a line segment equal to the sum of the other two sides along the ray of the angle.
- Join the end of this long segment to the other end of the base, forming a larger triangle.
- Construct the perpendicular bisector of this newly formed side. The point where this bisector intersects the long segment is the third vertex of the required triangle.
8. Where are the principles of geometric constructions used in real life?
The principles of geometric construction are fundamental to many real-world fields. For example:
- Architecture and Engineering: Architects use these principles to design blueprints for buildings, bridges, and rooms, ensuring angles are correct and structures are stable. For instance, creating perpendicular lines is crucial for layouts.
- Art and Design: Artists use construction techniques to create patterns, perspective, and symmetry in their work.
- Cartography (Map Making): Mapmakers use geometric principles to accurately plot locations and create precise maps.
- Computer Graphics: The algorithms used in computer-aided design (CAD) and video games are built on the logical steps of geometric constructions to render shapes and objects.
