CBSE Class 10 Mathematics HOTs Constructions

Please refer to CBSE Class 10 Mathematics HOTs Constructions. Download HOTS questions and answers for Class 10 Mathematics. Read CBSE Class 10 Mathematics HOTs for Chapter 11 Constructions below and download in pdf. High Order Thinking Skills questions come in exams for Mathematics in Class 10 and if prepared properly can help you to score more marks. You can refer to more chapter wise Class 10 Mathematics HOTS Questions with solutions and also get latest topic wise important study material as per NCERT book for Class 10 Mathematics and all other subjects for free on Studiestoday designed as per latest CBSE, NCERT and KVS syllabus and pattern for Class 10

Chapter 11 Constructions Class 10 Mathematics HOTS

Class 10 Mathematics students should refer to the following high order thinking skills questions with answers for Chapter 11 Constructions in Class 10. These HOTS questions with answers for Class 10 Mathematics will come in exams and help you to score good marks

HOTS Questions Chapter 11 Constructions Class 10 Mathematics with Answers

CBSE Class 10 Constructions HOTs. Higher Order Thinking Skills (HOTS) are part of the CBSE syllabus and form part of examinations. Students are requested to learn the HOTs for various subjects to score better in examinations, This portal has collection of important HOTs for all subjects and classes which have been made by experienced school teachers. Students should download and learn the HOTS.

TOPIC- Constructions (Class- X)

1. Draw a triangle ABC with sides BC = 6.3cm, AB = 5.2cm and ÐABC = 60° . Then construct a triangle whose sides are 43 times the corresponding sides of Δ ABC.
Solution: Steps of construction
1. Draw a line segment BC = 6.3cm
2. At B make < CBX = 60°
3. With B as centre and radius equal to 5.2 cm, draw an arc intersecting BX at A
4. Join AC, Then ABC is the required triangle
5. Draw any ray by making an acute angle with BC on the opposite side to the vertex A
6. Locate the points B1, B2, B3, B4 on BY so thatB1B2= B2B3= B3B4,
7. Join B3 to C and draw al line through B4 parallel to B3 C intersecting the extended line segment BC at C’.
8. Draw a line through C’ parallel to CA intersecting the extended line segment BA at A’ Thus A’BC’ is the required triangle.

class_10_maths_hot_03

2. Let ABC be a right triangle in which AB = 6cm, BC = 8cm and ÐB = 90° BD is the perpendicular from B on AC. The circle through B,C and D is drawn construct the tangents from A to this circle.
Solution: Steps of construction
1. Draw DABC with BC = 8cm, AB = 6cm and <B = 90°
2. Draw perpendicular BD from B to AC

3. Let O be the mid point of BC. Draw a circle with centre O and radius OB = OC. This circle will pass through the point D
4. Join AO and bisect AO
5. Draw a circle with centre O' and O' Aas radius cuts the previous circle at B and P
6. Join AP, AP and AB are required tangents drawn from A to the circle passing through B,C and D.

class_10_maths_hot_04

3. Draw a circle of radius 4 cm . Take a point P outside the circle. Without using the centre of the circle, draw two tangents to the circle from point P.
Solution: Steps of Construction:
i) Draw a line segment of 4 cm.
ii) Take a point P outside the circle and draw a secant PAB, intersecting the circle at A and B.
iii) Produce AP to C such that AP=CP
iv) Draw a semi-circle with CB as diameter.
v) Draw PD perpendicular to CB, intersecting the semi-circle at D.
vi) With P as centre and PD as radius draw arcs to intersect the given circle at and T’.

vii) Join PT and PT’. Then, PT and PT’ are the required tangents.

CBSE_Class_10_maths_construction_1

4. Construct a triangle ABC in which BC = 6cm, <A=600 and the attitude through A is 4.5cm. Measure the length of median through A. Write the steps of construction.
Solution:-
CBSE_Class_10_maths_construction_2
Steps of Construction: 
i) <CBP=600 BC = 6cm is drawn and is made downwards with BC of any length.
ii)<PBE=900 is drawn
iii) Perpendicular bisector RQ of BC is drawn which cut BC at M. and
intersect BE at O.
iv) Taking O as centre and OB as radius, a circle is drawn.
v)  ML = 4.5cm is cut from RQ.
vi) A line XY, parallel to BC is drawn through L to intersect the circle at A and A'.
AB, AC, A’B and A’C are joined.
ABC and A’BC are the required triangle
Median AM = A'M = 5.5cm (app.) 
 
5. Construct a triangle ABC in which BC = 5cm, <A700 and median AD through A is of length 3.5cm. Also, determine the length of the altitude drawn from A on the side BC (Write the steps of construction also).
 
Solution:-

CBSE_Class_10_maths_construction_3 

Steps Of Construction: 
i) BC = 5cm is drawn and is constructed downwards. ii)  BX is drawn perpendicular to BY. 
iii) Q is drawn perpendicular bisector if BC intersecting BX at O and cutting BC at E.  
iv) Taking O as a centre and OB as radius, a circle is drawn.
v)  Taking E as centre and radius equal to 3.5cm, arc is drawn to cut the circle at A. 
vi) AC and AB are joined 
vii)AD is drawn perpendicular to BC from A to cut BC at D. viii) By measuring we find that AD = 3cm. 
 
6. ΔABC˜ Draw a  to a equilateral ΔPQR with side 5cm such that each of its sides is 6/7th of the corresponding side of ΔPQR Also draw the circumcircle of ΔABC .

Solution:-

 CBSE_Class_10_maths_construction_4

Steps Of Construction:  
i) A ray QX is drawn making any angle with QR and opposite to P. 
ii)  Starting from Q, seven equal line segments QQ1, Q1R2, Q2Q3, Q3Q4, Q4Q5, Q5Q6, Q6Q7 are cut of from QX. 
iii) RQ7 is joined and a line CQ6 is drawn parallel to RQ4 to intersect QR at C. 
iv) Line CA is drawn parallel to PR. 
ABC is the required triangle.  
 
7. Construct a triangle ABC in which BC = 6cm, <=A600and median AD = 5cm. Also construct another triangle BPQ similar to triangle BCA such that the side BP = 3/2BC. Solution:-

 CBSE_Class_10_maths_construction_5

Steps Of Construction:  
i)   A line segment BC of length 6cm is drawn.
ii)  At B, <CBX=600is drawn on downwards.
iii) At B, CBSE_Class_10_maths_construction_11 is drawn 
iv) Perpendicular bisector of BC is drawn which intersect BY at O and BC at D. 
v)  Taking O as a center and OB as a radius a circle passing through B and C is drawn. 
vi) Taking D as a centre and radius 5cm an arc is drawn to intersect the circle at A. 
vii)AB and AC are joined. The required triangle is ABC. 
viii) Taking C as centre and CD as radius an arc is drawn to intersect BC produced at P such that BP = 3/2BC. 
ix) Through P, PQ is drawn parallel to CA meeting BA produced at Q.
x)  BPQ is the required triangle similar to triangle BCA.
 
8. Construct a quadrilateral ABCD in which AB = 2.5cm, BC = 3.5cm, AC = 4.2cm, CD = 3.5cm and AD = 2.5cm. Construct another quadrilateral AB’C’D’ with diagonal AC’ = 6.3cm such that it is similar to quadrilateral ABCD.
 
Solution:-

CBSE_Class_10_maths_construction_6

 

Steps Of Construction:  
i) A line segment Ac = 4.2cm is drawn. 
ii)  With A as a centre and radius 2.5cm, two arcs, one above AC and one below AC are drawn. 
iii) With C as centre and radius 3.5cm, two arcs arc drawn intersecting previous arcs at B and D./li> 
iv) AB, AD, BC and CD are joined ABCD is the required quadrilateral. 
v)  Taking A as a centre and radius 6.3cm an arc is drawn to intersect AC produced at C’. 
vi) Through C’, C’B’ and C’D’ are drawn parallel to CB and CD respectively. 
AB’C’D’ is the required quadrilateral similar to ABCD.
 
MORE QUESTION
 
Constructions
Key points
1. Construction should be neat and clean and as per scale given in question.
2. Steps of construction should be provided only to those questions where it is mentioned.
 
Questions
 
3 marks questions
Q. 1 Draw a line segment 14 cm long and find a point which divideds it in the 4 : 3. Also write the steps of construction.
 
Q. 2 Divide a 8 cm long line segment in the ratio 1 : 3. Also write the steps of construction.
 
Q. 3 Draw a line segment AB = 6.5 cm and find the point 'x' on it which divides it in the ratio 1 : 4. By actual measurement find AX / BX .
 
Q. 4 Draw a line segment AB = 9 cm and locate a point C on AB such that 4× AC = 5× BC.
 
Q. 5 Construct a circle C (0, 3). Take a point P at a distance of 6.5 cm from the centre. Construct the tangents to the circle from point P. Also write the steps of construction.
 
Q. 6 Mark a point P outside a circle C (0, 2.4) such that OP = 5 cm. Draw two tangents PA and PB to the circle from point P. Also write the steps of construction.
 
Q. 7 Draw a line segment BC = 7.5 cm. Find the point P on BC such that BP : PC = 2 : 3. Measure the length of BP and PC. Also write the steps of construction.
 
Q. 8 Construct a triangle AB'C' similar to given ΔABC such that each of its sides is 2 /3 rd of the corresponding sides of the ΔABC. It is given that AB = 6 cm, BC = 5 cm and AC = 6 cm. Also write the steps of construction.
 
Q. 9 Construct a triangle X 'YZ ' similar to given triangle XZY with its sides 1½ times that of the corresponding sides of a ΔXYZ . If is given that XY = 5 cm, YX = 7.4 cm and ∠XYZ = 740 . Also write the steps of constructions.
 
Q. 10 Construct an isosecles triangle with base 7 cm and vertical angle 1200 . Construct a triangle similar to given triangle with its corresponding sides being 4/3 times those of given triangle.
 
Q. 11 Construct a triangle A'BC' similar to given ΔABC with its sides equal to 1/3rd of its corresponding sides. It is given that ∠B = 900 , AB = 6 cm and BC = 8 cm.
 
Q. 12 Draw ΔABC with BC = 8 cm, ∠ABC = 450 and ∠BAC = 1050 . Then construct a triangle whose sides are 2 / 3 times the corresponding sides of the ΔABC .
 
Q. 13 Draw two tangents from the end points of diameter if the radius of the circle is 3 cm. Are these tangents parallel? Give reason.
 
Q. 14 Construct ΔPQR in which PQ = 7 cm, ∠Q = 500 and altitude RM to PQ is equal to 4.5 cm. Construct a ΔP'QR' similar to ΔPQR having each of its side 2/3 rd of the corresponding sides of ΔPQR . Also write the steps of construction.
 
Q. 15 Construct a ΔPQR in which PQ = 6 cm, ∠Q = 700 and altitude PS = 4 cm. Also construct a ΔPBC ∼ ΔPQR such that each side of ΔPBC is 1.8 times that of the corresponding sides of ΔPQR .
 
Q. 16 Draw a circle C (0, 2.5) P and Q are points on the circle such that ∠POQ =1200 . Construct tangents to the circle at P and Q to meet at a point R. Write measure ∠PRQ. What is the value of ∠POQ +∠PRQ ?
 
Q. 17 Draw a circle with centre D and radius 3 cm. Draw two tangent segments XY and XY ' from an exterior point X such that ∠YXY ' = 450 . Also write the steps of constructions.
 
Q. 18 Construct an equilateral triangle PQR with side 6 cm. Construct another triangle ΔP'QR' ∼ ΔPQR such that  PQ/P'Q = 1/' 2 . Is ΔP'QR' an equilateral triangle?
 
Q. 19 Draw a circle of radius 4.2 cm. Extend the diameter to both the sides to the points P and Q such that each point is at a distance of 7 cm from the centre. Draw the tangent to the circle from these two points P and Q?
 
Q. 20 Draw a line segment AB = 9 cm. With A and B as centres draw circles of radius 5 cm and 3 cm respectively. Construct tangent to each circle from the centre of the other circle.
 
Q. 21 Draw ΔABC with BC = 6 cm, AB = 5 cm and ∠ABC = 450 . Construct ΔA'B'C similar to ΔABC whose sides are 1*1/2 times the corresponding sides of the ΔABC.
 
1. Construct a DABC in which ÐB=120°, BA= 4cm and BC=5 cm. Construct another DAB’C’similar to DABC such that AB’= AB = 5/4
 
2. Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 45°.
 
3. Construct a DABC in which AB = 4.8 cm, BC = 6 cm and AC = 5.5 cm. Draw another triangle whose sides are 1 ½ times the corresponding sides of the given triangle.
Chapter 01 Real Numbers
CBSE Class 10 Maths HOTs Number Systems
Chapter 02 Polynomials
CBSE Class 10 Maths HOTs Polynomials
Chapter 03 Pair of Linear Equations in Two Variables
CBSE Class 10 Maths HOTs Pair Of Linear Equations In Two Variables
Chapter 04 Quadratic Equation
CBSE Class 10 Maths HOTs Quadratic Equations
Chapter 05 Arithmetic Progressions
CBSE Class 10 Maths HOTs Arithmetic Progressions
Chapter 06 Triangles
CBSE Class 10 Maths HOTs Similar Triangles
Chapter 07 Coordinate Geometry
CBSE Class 10 Maths HOTs Co-Ordinate Geometry
Chapter 08 Introduction to Trigonometry
CBSE Class 10 Maths HOTs Trigonometry
Chapter 09 Some Applications of Trigonometry
CBSE Class 10 Maths HOTs Heights And Distances
Chapter 10 Circles
CBSE Class 10 Maths HOTs Circles
Chapter 11 Constructions
CBSE Class 10 Mathematics HOTs Constructions
Chapter 12 Areas Related to Circles
CBSE Class 10 Maths HOTs Area related to Circle
Chapter 13 Surface Areas and Volumes
CBSE Class 10 Maths HOTs Conversion Of Solids
CBSE Class 10 Maths HOTs Mensuration
CBSE Class 10 Maths HOTs Surface Area and Volumes
Chapter 14 Statistics
CBSE Class 10 Maths HOTs Statistics
Chapter 15 Probability
CBSE Class 10 Maths HOTs Probability
More HOTs for Class 10 Mathematics
CBSE Class 10 Maths HOTs Question Bank Set B
CBSE Class 10 Maths HOTs Question Bank Set C
CBSE Class 10 Maths HOTs Question Bank Set D
CBSE Class 10 Maths HOTs Question Bank Set E

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CBSE Class 10 Mathematics Chapter 11 Constructions HOTS

We hope students liked the above HOTS for Chapter 11 Constructions designed as per the latest syllabus for Class 10 Mathematics released by CBSE. Students of Class 10 should download the High Order Thinking Skills Questions and Answers in Pdf format and practice the questions and solutions given in above Class 10 Mathematics  HOTS Questions on daily basis. All latest HOTS with answers have been developed for Mathematics by referring to the most important and regularly asked topics that the students should learn and practice to get better score in school tests and examinations. Studiestoday is the best portal for Class 10 students to get all latest study material free of cost.

HOTS for Mathematics CBSE Class 10 Chapter 11 Constructions

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Chapter 11 Constructions HOTS Mathematics CBSE Class 10

All HOTS given above for Class 10 Mathematics have been made as per the latest syllabus and books issued for the current academic year. The students of Class 10 can refer to the answers which have been also provided by our teachers for all HOTS of Mathematics so that you are able to solve the questions and then compare your answers with the solutions provided by us. We have also provided lot of MCQ questions for Class 10 Mathematics in the HOTS so that you can solve questions relating to all topics given in each chapter. All study material for Class 10 Mathematics students have been given on studiestoday.

Chapter 11 Constructions CBSE Class 10 HOTS Mathematics

Regular HOTS practice helps to gain more practice in solving questions to obtain a more comprehensive understanding of Chapter 11 Constructions concepts. HOTS play an important role in developing an understanding of Chapter 11 Constructions in CBSE Class 10. Students can download and save or print all the HOTS, printable assignments, and practice sheets of the above chapter in Class 10 Mathematics in Pdf format from studiestoday. You can print or read them online on your computer or mobile or any other device. After solving these you should also refer to Class 10 Mathematics MCQ Test for the same chapter

CBSE HOTS Mathematics Class 10 Chapter 11 Constructions

CBSE Class 10 Mathematics best textbooks have been used for writing the problems given in the above HOTS. If you have tests coming up then you should revise all concepts relating to Chapter 11 Constructions and then take out print of the above HOTS and attempt all problems. We have also provided a lot of other HOTS for Class 10 Mathematics which you can use to further make yourself better in Mathematics.

Where can I download latest CBSE HOTS for Class 10 Mathematics Chapter 11 Constructions

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