Class 9 Exam  >  Class 9 Notes  >  RD Sharma Solutions for Class 9 Mathematics  >  RD Sharma Solutions -Ex-17.2, Constructions, Class 9, Maths

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics PDF Download

Q1. Draw an angle and label it as ∠BAC. Construct another angle, equal to ∠BAC

 Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics
Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw an angle ABC and a line segment QR.
  2. With center A and any radius, draw an arc which intersects ∠BACat E and D.
  3. With Q as a centre and same radius draw an arc which intersects QR at S.
  4. With S as center and radius equal to DE, draw an arc which intersects the previous arc at T.
  5. Draw a line segment joining Q and T.

Therefore ∠PQR= ∠BAC

 

Q2. Draw an obtuse angle. Bisect it. Measure each of the angles so formed.

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw an angle ∠ABC of 1200.
  2. With B as a centre and any radius, draw an arc which intersects AB at P and BC at Q.
  3. With P as center and radius more than half of PQ draw an arc.
  4. With Q as a center and same radius draw an arc which cuts the previous arc at R.
  5. Join BR.

Therefore ∠ABR=  ∠RBC=  600

  

Q3. Using your protractor, draw an angle of 1080. With this given angle as given, draw an angle of 540.

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics 

Steps of construction:

  1. Draw an angle ABC of 1080.
  2. With B as the center and any radius draw an arc which intersects AB at P and BC at Q.
  3. With P as center and radius more than half of PQ draw an arc.
  4. With Q as the centre and same radius draw an arc which intersects the previous arc at R.
  5. Join BR.

Therefore ∠RBC=  540

 

Q4. Using the protractor, draw a right angle. Bisect it to get an angle of measure 450.

 Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw an angle ABC of 900.
  2. With B as the centre and any radius draw an arc which intersects AB at P and BC at Q.
  3. With P as center and radius more than half of PQ draw an arc.
  4. With Q as center and same radius draw an arc which intersects the previous arc at R.
  5. Join RB.

Therefore ∠RBC=  450

 

Q5. Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisecting rays are perpendicular to each other.

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw two angles DCA and DCB forming linear pair
  2. With center C and any radius draw an arc which intersects AC at P and CD at Q and CB at R
  3. With center P and Q and any radius draw two arcs which intersect each other at S
  4. Join SC
  5. With Q and R as center and any radius draw two arcs which intersect each other at T
  6. Join TC

Therefore ∠SCT=  900.

 

Q6. Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line.

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of Construction:

  1. Draw a pair of vertically opposite angle ∠AOC and ∠DOB.
  2. Keeping O as the center and any radius draw two arcs which intersect OA at P, OC at Q, OB at S and OD at R.
  3. Keeping P and Q as center and radius more than half of PQ draw two arcs which intersect each other at T.
  4. Join TO.
  5. Keeping R and S as center and radius more than half of RS draw two arcs which intersect each other at U.
  6. Join OU.

Therefore TOU is a straight line

  

Q7. Using rulers and compasses only, draw a right angle.

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw a line segment AB.
  2. Keeping A as the center and any radius draw an arc which intersects AB at C.
  3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D.
  4. Keeping D as the center and same radius draw an arc which intersects arc in (2) at E.
  5. Keeping E and D as center and radius more than half of ED draw arcs which intersect each other at F.
  6. Join FA.

Therefore ∠FAB=  900

 

Q8.Using rulers and compasses only, draw an angle of measure 1350.

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw a line segment AB and produce BA to C.
  2. Keeping A as the center and any radius draw an arc which intersects AC at D and AB at E.
  3. Keeping D and E as center and radius more than half of DE draw arcs which intersect each other at F.
  4. Join FA which intersects the arc in (2) at G.
  5. Keeping G and D as center and radius more than half of GD draw arcs which intersect each other at H.
  6. Join HA.

Therefore ∠HAB=  1350

 

Q9. Using a protractor, draw an angle of measure 720. With this angle as given draw angles of measure 360and 540.

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw an ∠ABC of 720 with the help of a protractor.
  2. Keeping B as center and any radius draw an arc which intersects AB at D and BC at E.
  3. Keeping D and E as center and radius more than half of DE draw two arcs which intersect each other at F.
  4. Join FB which intersects the arc in (2) at G.
  5. Keeping D and G as center and radius more than half of DG draw two arcs which intersect each other at H
  6. Join HB

Therefore ∠HBC=  540

∠FBC=  360

 

Q10. Construct the following angles at the initial point of a given ray and justify the construction:

  1. 450
  2. 900

Answers

  1. 450

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw a line segment AB and produce BA to C.
  2. Keeping A as the center and any radius draw an arc which intersects AC at D and AB at E.
  3. Keeping D and E as center and radius more than half of DE draw arcs which intersect each other at F.
  4. Join FA which intersects the arc in (2) at G.
  5. Keeping G and E as center and radius more than half of GE draw arcs which intersect each other at H.
  6. Join HA.

Therefore ∠HAB=  450 

2. 900

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction

  1. Draw a line segment AB.
  2. Keeping A as the center and any radius draw an arc which intersects AB at C.
  3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D.
  4. Keeping D as the center and same radius draw an arc which intersects arc in (2) at E.
  5. Keeping E and D as center and radius more than half of ED draw arcs which intersect each other at F.
  6. Join FA.

Therefore ∠FAB=  900

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

 

Q11. Construct the angles of the following measurements:

  1. 300
  2. 750
  3. 1050
  4. 1350
  5. 150
  6. Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

ANSWERS: 

  1. 300

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw a line segment AB.
  2. Keeping A as the centre and any radius draw an arc which intersects AB at C.
  3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D.
  4. Keeping D and C as center and radius more than half of DC draw arcs which intersect each other at E.
  5. Join EA.

Therefore ∠EAB=  300

 

2. 750

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw a line segment AB
  2. Keeping A as center and any radius draw an arc which intersects AB at C
  3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D
  4. Keeping D as center and same radius draw an arc which intersects arc in (2) at E
  5. Keeping E and D as center and radius more than half of ED, draw arcs intersecting each other at F
  6. Join FA which intersects arc in (2) at G
  7. Keeping G and D as center and radius more than half of GD draw arcs intersecting each other at H
  8. Join HA

Therefore ∠HAB=  750

 

3.1050

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw a line segment AB.
  2. Keeping A as the center and any radius draw an arc which intersects AB at C.
  3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D.
  4. Keeping D as the centre and same radius draw an arc which intersects arc in (2) at E.
  5. Keeping E and D as center and radius more than half of ED draw arcs which intersect each other at F.
  6. Join FA which intersects arc in (2) at G.
  7. Keeping E and G as center and radius more than half of EG draw arcs which intersect each other at H.
  8. Join HA.

Therefore ∠HAB=  1050  

 

4. 1350

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw a line segment AB and produce BA to C.
  2. Keeping A as the center and any radius draw an arc which intersects AC at D and AB at E.
  3. Keeping D and E as center and radius more than half of DE draw arcs which intersect each other at F.
  4. Join FA which intersects the arc in (2) at G.
  5. Keeping G and D as center and radius more than half of GD draw arcs which intersect each other at H
  6. Join HA.

Therefore ∠HAB=  1350 

 

5. 150

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw a line segment AB.
  2. Keeping A as the centre and any radius draw an arc which intersects AB at C.
  3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D.
  4. Keeping D and C as center and radius more than half of DC draw arcs which intersect each other at E.
  5. Join EA which intersects arc in (2) at F.
  6. Keeping F and C as center and radius more than half of FC draw arcs which intersect each other at G.
  7. Join GA.

Therefore ∠GAB=  150

 

6. Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw a line segment AB.
  2. Keeping A as the center and any radius draw an arc which intersects AB at C.
  3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D.
  4. Keeping D as the centre and same radius draw an arc which intersects arc in (2) at E.
  5. Keeping E and D as center and radius more than half of ED draw arcs which intersect each at F.
  6. Join FA which intersects arc in (2) at G.
  7. Keeping G and C as center and radius more than half of GC draw arcs intersecting each other at point H.
  8. Join HA which intersects the arc in (2) at a point I.
  9. Keeping I and C as center and radius more than half of IC draw arcs intersecting each other at point J.
  10. Join JA.

Therefore ∠JAB=  Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

The document Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.
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FAQs on Ex-17.2, Constructions, Class 9, Maths RD Sharma Solutions - RD Sharma Solutions for Class 9 Mathematics

1. How can I access the RD Sharma Solutions for Class 9 Maths Chapter 17.2 on Constructions?
Ans. You can access the RD Sharma Solutions for Class 9 Maths Chapter 17.2 on Constructions by either purchasing the physical book or accessing it online through various educational websites or e-learning platforms.
2. Are the RD Sharma Solutions for Class 9 Maths Chapter 17.2 on Constructions available for free online?
Ans. No, the RD Sharma Solutions for Class 9 Maths Chapter 17.2 on Constructions are not available for free online. They are copyrighted materials and need to be purchased either physically or through authorized online platforms.
3. How can the RD Sharma Solutions for Class 9 Maths Chapter 17.2 on Constructions help me in my exam preparation?
Ans. The RD Sharma Solutions for Class 9 Maths Chapter 17.2 on Constructions provide step-by-step solutions to all the questions in the textbook. By referring to these solutions, you can understand the concepts better, practice different types of questions, and improve your problem-solving skills, which will ultimately help you in your exam preparation.
4. Can the RD Sharma Solutions for Class 9 Maths Chapter 17.2 on Constructions be used as a standalone study material?
Ans. The RD Sharma Solutions for Class 9 Maths Chapter 17.2 on Constructions are meant to be used as a supplement to the textbook. While they provide detailed solutions to the questions, it is recommended to study the concepts from the textbook first and then use the solutions for practice and better understanding.
5. Are the RD Sharma Solutions for Class 9 Maths Chapter 17.2 on Constructions sufficient for scoring good marks in the exam?
Ans. The RD Sharma Solutions for Class 9 Maths Chapter 17.2 on Constructions are a valuable resource for exam preparation, but they should not be the only source of study. It is important to understand the concepts, practice different types of questions, and solve additional exercises to ensure a thorough preparation and to score good marks in the exam.
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