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Construction is an important chapter in Class 9 Mathematics Syllabus that focuses on drawing accurate geometric figures using only a ruler and compass. In this chapter, students learn how to construct angles, triangles, perpendicular bisectors and other basic geometric shapes step by step. These constructions help in understanding the properties of shapes and improve logical thinking and accuracy, which are essential for exams and higher-level mathematics.
Today we will share with you Important notes of the Class Construction . We will also give some examples of questions so students can learn how they can solve statistics chapter questions. This Chapter is extremely easy to study. Let's study this chapter in a sequence -wise style.
Class 9 Construction Notes PDF Download
These notes on class 9 construction notes are prepared to help students understand geometric constructions in a clear and step-by-step manner. All important methods and concepts are explained simply for easy practice and quick revision. For the complete notes, download them from below.
What is Construction ?
In geometry, construction is the process of drawing figures by the help of paper and tol lille compass. To draw any figure in geometry we mostly use a compass to make accurate drawing figures. We also use a protractor and a graduate scale to measure the length of our drawing diagrams.
Basic Rules of Construction
- While drawing we cannot measure lengths or angles directly with a ruler or protector. While drawing use the compass and ruler without markings.
- All constructions must be exact in measuremnet, not approximate.For example - Constructing a 60 degree angle using a compass, not using measuring with a protractor.
- Do not use sets - squares, protractor, dividers etc unless allowed in a specific problem.
- Always geometrical principles while drawing figures. Principles like perpendicular bisector, angle bisector and constructing parallel lines while drawing figures should always be followed.
- Use only question data to draw figures don't add anything on your own
Steps of Construction:
- Draw a line segment AB = x cm.
- Make an acute ∠BAX at the end A of AB.
- Use a compass of any radius and mark off arcs. Take (m + n) points A1, A2, … Am, Am+1, …, Am+n along AX such that AA1 = A1A2 = … = Am+n-1 , Am+n
- Join Am+nB.
- Passing through Am, draw a line AmP || Am+nB to intersect AB at P. The point P so obtained is the A required point which divides AB internally in the ratio m : n.
Construction of a Tangent at a Point on a Circle to the Circle when its Centre is Known
Construction 1
Draw a circle with centre O of the given radius.
Take a given point P on the circle.
Join OP.
Construct ∠OPT = 90°.
Produce TP to T’ to get TPT’ as the required tangent.
Construction 2
- Draw a circle with centre O.
- Join the centre O to the given external point P.
- Draw a right bisector of OP to intersect OP at Q.
- Taking Q as the centre and OQ = PQ as radius, draw a circle to intersect the given circle at T and T’.
- Join PT and PT’ to get the required tangents as PT and PT’.
Construction 3
(i) Draw a secant PAB to intersect the circle at two points A and B.
(ii) Produce AP to a point C, such that PA = PC.
(iii) With BC as a diameter, draw a semi-circle.
(iv) Draw PD ⊥ CB, intersecting the semi-circle drawn in step (iii) at D.
(v) Taking PD as radius and P as centre, draw arcs to intersect the given circle at T and T’.
(vi) Draw rays PT and VT’. Rays PT and PT’ are the required tangents.
In sum, these are the rapid revision notes. If Students keep practicing this chapter they will surely learn to solve all types of statistics problems .
By revising this note's students will be step ahead in the revision of exams these notes guide you to study faster during the exam time.
FAQs
Q1. What does “construction” actually mean in geometry?
Ans. Construction means creating geometric figures using logic and properties, not measurements. Every line, angle or shape is drawn based on mathematical reasoning, proving that the figure is correct by principle rather than guesswork.
Q2. Why are only a compass and ruler used in constructions?
Ans. A compass and ruler help students rely on geometric properties instead of numerical measurements. This trains the mind to think logically and understand relationships between points, lines and angles.
Q3. How do constructions help in understanding geometry better?
Ans. When students construct a figure themselves, they see how different parts of a shape are connected. This visual learning makes concepts like perpendicular bisectors, angle bisectors and tangents easier to understand and remember.
Q4. Why is accuracy so important in construction drawings?
Ans. Accuracy ensures that the geometric principles are correctly applied. A small error can change the properties of a figure, so precise construction helps students develop focus and discipline in mathematical thinking.
Q5. How is construction useful beyond Class 9 mathematics?
Ans. Construction builds a strong foundation for advanced geometry, coordinate geometry and even real-life applications like architecture and engineering. It improves spatial reasoning and problem-solving skills used throughout higher mathematics.
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