Construction Class 10 NCERT Solutions
NCERT Solutions for class 10 maths construction are thoroughly explained hare. These solutions are created by expert team at Careers360 keeping in mind of latest syllabus and pattern of CBSE 2023-24. These NCERT solutions provide a step-by-step approach to solving all questions and comprehensively discussed them in easy and simple language. These NCERT solutions for class 10 are created under NCERT guidelines, are designed to aid students in preparing for their board exams.
NCERT Solutions for Class 10 Maths Chapter 11 Constructions Get free access to construction class 10 solutions on Careers360 to improve your CBSE exam preparation. Each question of the NCERT exercises is solved using diagrams with a clear step-by-step procedure for the class 10 construction solution. These NCERT solutions can help students improve their understanding and clarify any doubts they may have. Also Students can download NCERT solutions for class 10 maths chapter 11 pdf using the link given below.
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NCERT Solutions for Class 10 Maths Construction PDF Free Download
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NCERT Solutions for class 10 maths construction - Important Points
Determination of a Point Dividing a Line Segment Internally:
Given a line segment AB, a point P can be determined that divides AB internally in the ratio M : N using the formula: AP/AB = M/(M+N)
Construction of a Tangent to a Circle with Known Center - A tangent can be constructed at a specific point P on a circle with a known centre O. The tangent line is perpendicular to the radius OP.
Construction of a Tangent to a Circle without Known Center - Even without knowing the exact center of the circle, you can construct a tangent at a point P on the circle using geometric methods.
Construction of Tangents from an External Point to a Circle with Known Center - Tangents can be drawn from an external point E to a circle with a known centre O. The tangent lines are equal in length and angles between the radius and tangents are right angles.
Construction of Tangents from an External Point to a Circle without Known Center - Even without knowing the circle's center, you can construct tangents from an external point E to the circle using specific techniques.
Construction of a Similar Triangle with Given Scale Factor (m/n), m < n:
To construct a triangle similar to a given triangle ABC, but scaled down with a ratio m/n, the corresponding sides of the new triangle are m times smaller than the sides of ABC.
Construction of a Similar Triangle with Given Scale Factor (m/n), m > n:
Similarly, if the scale factor m/n is greater than 1, the corresponding sides of the new triangle are m times larger than the sides of ABC.
Free download NCERT Solutions for class 10 maths construction PDF for CBSE Exam.
NCERT Solutions for construction class 10 (Intext Questions and Exercise)
NCERT Solutions for Maths Chapter 11 Construction Class 10th Excercise: 11.1
In each of the following, give the justification of the construction also:
Q1 Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.
Answer:
Steps of construction:-
(i) Draw a line segment AB of measurement 7.6 cm (length).
(ii) Now draw an acute angle AC with line segment AB.
(iii) Now cut 13 equal points on the line AC where the zeroth point is A.
(iv) Join the 13th point with point B. So the new line is BA 13 .
(v) Now, from point A 5 draw a line parallel to BA 13 on line AB. Name the point as D.
The point D is the required point which divides the line segment in the ratio of 5: 8.
The length of the two parts obtained is 2.9 cm and 4.7 cm for AD and DB respectively.
Justification:- In the figure, we can see two similar triangles: and
Thus .
Q3 Construct a triangle with sides 5 cm, 6 cm, and 7 cm and then another triangle whose sides are 7 / 5 of the corresponding sides of the first triangle.
Answer:
Steps of construction are:-
(i) Firstly draw a line segment AB of length 5 cm.
(ii) Now cut an arc of radius 6 cm from point A and an arc of 7 cm from point B.
(iii) Name the point of intersection of arcs to be point C.
(iv) Now join point AC and BC. Thus ABC is the required triangle.
(v) Draw a line AD which makes an acute angle with AB and is opposite of vertex C.
(vi) Cut seven equal parts of line AD namely AA 1 , AA 2 , AA 3 , AA 4 , AA 5 , AA 6 , AA 7 ,.
(vii) Now join A 5 to B. Draw a line A 7 B' parallel to A 5 B.
(viii) And then draw a line B'C' parallel to BC.
Hence AB'C' is the required triangle.
NCERT Solutions for Chapter 11 Class 10 construction Excercise: 11.2
Q1 In each of the following, give also the justification of the construction:
Draw a circle of radius 6 cm. From a point 10 cm away from its center, construct the pair of tangents to the circle and measure their lengths.
Answer:
Steps of construction:-
(i) Taking point O as center draw a circle of radius 6 cm.
(ii) Now, name a point P which is 10 cm away from point O. Join OP.
(iii) Draw a perpendicular bisector of OP name the intersection point of bisector and OP as O'.
(iv) Now draw a circle considering O' as center and O'P as the radius.
(v) Name the intersection point of circles as Q and R.
(vi) Join PQ and PR. These are the required tangents.
(vii) Measure lengths of PQ = 8cm and PR = 8cm
Q4 Draw a pair of tangents to a circle of radius 5 cm which is inclined to each other at an angle of 60°.
Answer:
Steps of construction:-
(i) Draw a circle with center O and radius 5 cm.
(ii) Now mark a point A on the circumference of the circle. And draw a line AP perpendicular to the radius OA.
(iii) Mark a point B on the circumference of the circle such that AOB = 120 o . (As we know, the angle at the center is double that of the angle made by tangents).
(iv) Join B to point P.
(v) AP and BP are the required tangents.
Construction Class 10 NCERT-Topics
To divide a line segment in the given ratio.
To construct a pair of tangents from an external point to a circle.
To construct a triangle similar to a given triangle as per a given scale factor which may be greater than 1 or less than 1.
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Feature of Solutions to Class 10 Maths NCERT Chapter 11 Constructions
- Construction Class 10 is one of the scoring chapters under the geometry unit. It is a part of geometry and it holds 15 marks in the final exams. There are 2 exercises with 14 questions in this NCERT Class 10 Maths chapter 11.
- In Class 9, we have done certain calculations and constructions using a compass and a straight edge (ruler), for example, construction of triangles, drawing the perpendicular bisector of a line segment and much more and also gave their justifications. In this NCERT Class 10 Maths chapter 11 Constructions , you will study some advanced constructions by using the concepts learnt in class 9 constructions.
- These M aths ch 11 class 10 solutions are about the construction of a line segment and a circle, division of a line segment and constructions of tangents to a circle using an analytical approach.
- Also, students have to write the steps of construction for each answer.
- In exercise 11.1 of NCERT class 10th Construction Solutions, you will study how to divide a line segment and in exercise 11.2 you will study the construction of tangents to a circle.
NCERT Solutions for Class 10 Maths - Chapter Wise
NCERT Solutions of Class 10 - Subject Wise
How to Use NCERT Solutions for Class 10 Maths Chapter 11 Constructions?
- Before coming to this NCERT Construction Class 10 Maths chapter 3, please ensure that you have done the construction chapter of Class 9.
Learn some basic constructions like angles, triangles, and circles using compass and scale.
After this, go through some examples available in Cass 10 Maths Construction.
After covering the above processes, you can come to the practice exercises.
While practising the question, If you feel some trouble in any problem then take the help of NCERT solutions for Class 10 Maths Chapter 11 Constructions.
NCERT Solutions for Class 10 Maths Chapter 3 pdf download will be available soon. Till then you can download the webpage to practice the questions offline.
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