Class 9 RD Sharma Solutions Chapter 17 Constructions Exercise 17.1 (original) (raw)

Last Updated : 23 Jul, 2025

In Class 9 Mathematics, Chapter 17 focuses on Construction which involves drawing geometric shapes, angles, and figures using a compass, ruler, and protractor. This chapter emphasizes precision and understanding geometric principles through practical drawing exercises. Exercise 17.1 covers basic construction problems that lay the foundation for the more complex constructions.

Constructions

Constructions refer to the method of drawing geometric shapes with the help of tools like a compass and ruler following specific mathematical procedures. This chapter helps students develop spatial reasoning and understand the fundamental properties of geometric figures by creating accurate representations of the various shapes and angles.

Question 1. Draw a line segment of length 8.6cm. Bisect it and measure the length of each part.

**Solution:

Steps of construction:

Step 1: Draw a line segment AB of 8.6cm.

Step 2: With center A and radius more than 1/2 AB, drawn arcs, one on each side of AB.

Step 3: With centre B and same radius, draw arcs cutting the previous arcs at P and Q.

Step 4: Now join in PQ

So, DC = BC = 4.3cm

Question 2. Draw a line segment AB of length 5.8cm. Draw the perpendicular bisector of this line segment.

**Solution:

Steps of construction:

Step 1: Draw a line segment AB of 5.8cm.

Step 2: With centre A radius more than 1/2 AB draw arcs with one on each side of AB.

Step 3: With centre B and same radius draw arcs cutting the previous arcs at P and Q.

Step 4: Now join PQ.

So, PQ is the perpendicular bisector of AB.

Question 3. 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?

**Solution:

Steps of construction:

Step 1: With centre O and radius 5cm draw a circle.

Step 2: Now draw a chord AB.

Step 3: With centre A and radius more than 1/2 AB draw arcs one on each side O.

Step 4: With centre B and same radius draw arcs cutting previous arcs at P and Q.

Step 5: Now join point P and Q.

So, the perpendicular bisector PQ of chord AB passes through the center of the circle

Question 4. 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 bisector of AB and CD. At what point do they intersect?

**Solution:

Steps of construction:

Step 1: With centre O and any radius, draw a circle.

Step 2: Draw two chords AB and CD.

Step 3: With centre A and radius more than 1/2 AB draw arcs, one on each side of AB.

Step 4: With centre B and same radius draw arcs cutting previous arcs at P and Q respective.

Step 5: Join PQ.

Step 6: With centre B and radius more than 1/2 DC draw arcs one on each side of DC.

Step 7: With centre C and same radius, draw arcs cutting previous arcs at R and S.

Step 8: Now join RS.

So, Both perpendicular bisectors PQ and RS intersect each other at the centre O of the circle.

Question 5. Draw a line segment of length 10cm and bisect it. Further, bisect one of the equal parts and measure its length.

**Solution:

Steps of construction:

Step 1: Draw a line segment AB of 10cm.

Step 2: With centre A and radius more than 1/2 AB, draw arcs one on each side of AB.

Step 3: With centre B and same radius draw arcs cutting previous arcs at P and Q respectively.

Step 4: Join PQ and which intersect AB at C.

Step 5: With centre A and radius more than 1/2 AC, draw arcs on each side of AC.

Step 6: With centre C and same radius, radius, draw arcs cutting previous arcs at R and S respectively.

Step 7: Now join RS and which intersect AC at D.

So, AD = 2.5cm

Question 6. Draw a line segment AB bisect it. Bisect one of the equal parts to obtain a line segment of length 1/4(AB).

**Solution:

Steps of construction:

Step 1: Draw a line segment AB.

Step 2:. With centre A and radius more than 1/2 AB, draw arcs one on each side of AB.

Step 3: With centre B and same radius, draw arcs cutting previous arcs at P and Q.

Step 4: Join PQ which intersects AB at C.

Step 5: With centre A and radius more than 1/2 AC, draw arcs one on each side of AC.

Step 6: Which centre C and same radius, draw arcs cutting previous arcs at R and S.

Step 7: Now join RS Which intersect AC at D.

So, AD = 1/4AB

Question 7. Draw a line segment AB and by ruler and compasses, obtain a line segment of length 3/4(AB).

**Solution:

Steps of construction:

Step 1: Draw a line segment AB.

Step 2: With centre A and radius more than 1/2 AB, draw arcs one on each side of AB.

Step 3: With centre B and same radius draw arcs cutting previous arcs at P and Q.

Step 4: Join PQ which intersect AB at C.

Step 5: With centre C and radius more than 1/2 CB, draw arcs, one on each side of CB.

Step 6: With centre B and same radius draw arcs cutting previous arcs at R and S.

Step 7: Join RS which intersect CB at D.

So, AD = 3/4 AB.

**Read More:

• Construction of Triangles
• Maths

Conclusion

Chapter 17 of RD Sharma's Class 9 Mathematics textbook focuses on the fundamental principles of the geometric constructions. Exercise 17.1 provides students with the hands-on practice in the constructing various geometrical figures using the compass and straightedge. The Mastery of these constructions forms the foundation for the more advanced topics in geometry ensuring that students develop both the precision and confidence in their mathematical skills.