Class 9 Exam  >  Class 9 Notes  >  RD Sharma Solutions for Class 9 Mathematics  >  RD Sharma Solutions -Ex-17.1, Constructions, Class 9, Maths

Ex-17.1, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics PDF Download

Q1. Draw a line segment of length 8.6cm. Bisect it and measure the length of each part.

 Ex-17.1, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw a line segment AB of 8.6cm.
  2. Keeping A as center and radius more than half of AB draw arcs on each side of AB.
  3. Keeping B as center and the same radius draw arcs on each side of AB cutting the previous arcs at P and Q respectively.
  4. Join the points P and Q which intersects AB at C.

Therefore AC= BC= 4.3cm

 

Q2. Draw a line segment AB of length 5.8cm. Draw the perpendicular bisector of this line segment.

Ex-17.1, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw a line segment AB of 5.8cm.
  2. Keeping A as center and radius more than half of AB draw arcs on each side of AB.
  3. Keeping B as center and the same radius draw arcs on each side of AB cutting the previous arcs at P and Q respectively.
  4. Join the points P and Q.

Hence PQ is the perpendicular bisector of AB

 

Q3. Draw a circle with center at point O and radius 5cm. Draw its chord AB, the perpendicular bisector of line segment AB. Does it pass through the center of the circle?

 Ex-17.1, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Keeping O as center and radius as 5cm draw a circle.
  2. Draw a chord AB.
  3. Keeping A as center and radius more than half of AB draw arcs one on each side of chord AB.
  4. Keeping B as center and the same radius draw arcs cutting the previous arcs at points P and Q respectively.
  5. Join the points P and Q.

Therefore the perpendicular bisector PQ of chord AB passes through the center of the circle.

 

Q4. Draw a circle with center at point O. Draw its two chords AB and CD such that AB is not parallel to CD. Draw the perpendicular bisectors of AB and CD. At what point do they intersect?

Ex-17.1, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Keeping O as the centre and any radius draw a circle.
  2. Draw two chords AB and CD.
  3. Keeping A as center and radius more than half of AB draw arcs, one on each side of AB.
  4. Keeping B as center and the same radius draw arcs cutting the previous arcs at point P and Q respectively.
  5. Join the points P and Q.
  6. Keeping D as center and radius more than half of DC draw arcs, one on each side of DC.
  7. Keeping C as center and the same radius draw arcs cutting the previous arcs at points R and S respectively.
  8. Join the points R and S.

Both the perpendicular bisectors PQ and RS intersect each other at the center O of the circle.

 

Q5. Draw a line segment of length 10cm and bisect it. Further, bisect one of the equal parts and measure its length.

Ex-17.1, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw a line segment AB of length 10cms.
  2. Keeping A as center and radius more than half of AB draw arcs one on each side of AB.
  3. Keeping B as center and same radius draw arcs cutting the previous arc at point P and Q respectively.
  4. Join P and Q which intersects AB at C.
  5. Keeping A as center and radius more than half of AC draw arcs on each side of AC.
  6. Keeping C as center and the same radius draw arcs cutting the previous arcs at points R and S respectively.
  7. Join points R and S which intersects AC at D.

 Therefore AD= 2.5cm

 

Q6. Draw a line segment AB bisect it. Bisect one of the equal parts to obtain a line segment of length Ex-17.1, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics(AB).

Ex-17.1, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw a line segment AB.
  2. With A as center and radius more than half of AB draw arcs, one on each side of AB.
  3. With B as the center and same radius draw arcs cutting the previous arcs at points P and Q respectively.
  4. Join P and Q which intersects AB at C.
  5. With A as center and radius more than half of AC draw arcs, one on each side of AC.
  6. With C as the center and same radius draw arcs cutting the previous arcs at R and S respectively.
  7. Join points R and S which intersects AC at D.

Therefore AD= Ex-17.1, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics(AB)

 

Q7. Draw a line segment AB and by ruler and compasses, obtain a line segment of length Ex-17.1, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics(AB).

 Ex-17.1, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Steps of construction:

  1. Draw a line segment AB.
  2. With A as center and radius more than half of AB draw arcs, one on each side of AB.
  3. With B as the center and same radius draw arcs cutting the previous arcs at points P and Q respectively.
  4. Join P and Q which intersects AB at C.
  5. With A as center and radius more than half of AC draw arcs, one on each side of AC.
  6. With C as the center and same radius draw arcs cutting the previous arcs at R and S respectively.
  7. Join points R and S which intersects AC at D.

Therefore AD= Ex-17.1, Constructions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics((AB)

The document Ex-17.1, 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-17.1, Constructions, Class 9, Maths RD Sharma Solutions - RD Sharma Solutions for Class 9 Mathematics

1. What are RD Sharma Solutions?
Ans. RD Sharma Solutions are a set of comprehensive and step-by-step solutions to the questions and exercises present in the RD Sharma textbook. These solutions are designed to help students understand and solve mathematical problems effectively.
2. What is Ex-17.1 in RD Sharma Solutions?
Ans. Ex-17.1 in RD Sharma Solutions refers to Exercise 17.1 in the textbook. This exercise contains a set of questions related to the topic of constructions in mathematics. It focuses on teaching students how to construct various geometrical figures using a compass, ruler, and other tools.
3. Which class is RD Sharma Solutions - Ex-17.1 meant for?
Ans. RD Sharma Solutions - Ex-17.1 is meant for Class 9 students. This exercise is a part of the mathematics curriculum for Class 9 and covers the topic of constructions.
4. What does the term "construction" mean in mathematics?
Ans. In mathematics, the term "construction" refers to the process of creating or drawing geometrical figures using specific tools such as a compass, ruler, and protractor. It involves following a set of precise steps to accurately create figures like triangles, quadrilaterals, circles, etc.
5. How can RD Sharma Solutions - Ex-17.1 help students?
Ans. RD Sharma Solutions - Ex-17.1 can help students in multiple ways. It provides detailed solutions to the exercise questions, guiding students on the step-by-step construction process. These solutions help students understand the concepts better and improve their problem-solving skills in geometry. Additionally, practicing with these solutions can also enhance their overall performance in mathematics exams.
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