RD Sharma Solutions Class 6 Maths Chapter 19 Geometrical Constructions

Chapter 19 of the RD Sharma Solutions Class 6 Maths focuses on an exciting and hands-on area of mathematics—Geometrical Constructions. This chapter helps students understand how to create accurate shapes and figures using only a ruler and compass. Aligned with the CBSE syllabus and closely following the concepts in the NCERT Solutions Class 6 Maths, this chapter builds a strong foundation in geometry through practical drawing techniques.

Through simple step-by-step methods, students will learn how to construct lines, angles, perpendicular bisectors, and more. The RD Sharma solutions make these concepts easy to follow, with clear diagrams and explanations that support both classwork and self-study.

Whether you're preparing for exams or just want to strengthen your geometry skills, this chapter offers everything you need in a clear and engaging way.

RD Sharma Solutions Class 6 Maths Chapter 19 Geometrical Constructions

Chapter 19 – Geometrical Constructions in RD Sharma Solutions Class 6 Maths introduces students to the basics of geometric drawing using simple tools like a ruler and compass. This chapter includes several practical exercises that guide learners through the step-by-step process of constructing lines, angles, perpendiculars, and angle bisectors. 

Key topics covered include drawing a line segment of a given length, constructing angles such as 30°, 60°, 90°, and 120° without a protractor, and bisecting angles and line segments accurately. 

RD Sharma Solutions of Class 6 Maths Chapter 19 Exercises

1. Exercise 19.1
2. Exercise 19.2
3. Exercise 19.3
4. Exercise 19.4
5. Exercise 19.5
6. Exercise 19.6

Through these exercises, students will learn how to apply measurement and drawing techniques with precision—skills that are foundational for higher-level geometry. 

RD Sharma Solutions for Class 6 Maths Chapter 19 | Free PDF Download

Looking to master basic constructions in geometry? The RD Sharma Solutions Class 6 Maths Chapter 19 – Geometrical Constructions are now available for free PDF download to support your learning. These step-by-step solutions are designed to help students understand the essential techniques of drawing geometric shapes using only a ruler and compass.

Aligned with the CBSE syllabus and ideal for exam preparation, these solutions simplify complex ideas, making them easier to practice and apply. Students will explore key concepts like drawing lines, angles, and bisectors accurately, as explained in the NCERT Solutions for Class 6 Maths as well.

Each construction is clearly explained and supported with diagrams. With the help of a scale and protractor, learners can also check the accuracy of their constructions, ensuring their understanding is both visual and precise.

RD Sharma Solutions Class 6 Maths Chapter 19 Geometrical Constructions

1. Which instrument is not required for basic geometrical constructions?
A. Compass
B. Ruler
C. Divider
D. Protractor
Answer: C. Divider

2. To construct a 60° angle, which of the following methods is used?
A. Use a protractor directly
B. Construct an equilateral triangle
C. Draw a 90° angle and subtract 30°
D. None of the above
Answer: B. Construct an equilateral triangle

3. A perpendicular bisector divides a line segment into:
A. Two equal angles
B. Two equal line segments at 90°
C. Two different parts
D. A triangle
Answer: B. Two equal line segments at 90°

4. Which angle cannot be constructed using only a compass and straightedge?
A. 60°
B. 90°
C. 105°
D. 100°
Answer: D. 100°

5. To bisect a given angle, the compass is used to:
A. Measure the angle
B. Divide the angle into two equal parts
C. Draw a perpendicular line
D. Join endpoints of the angle
Answer: B. Divide the angle into two equal parts

6. What is the first step in constructing a triangle when all sides are given?
A. Draw any angle
B. Measure height
C. Draw the base line
D. Use a protractor
 Answer: C. Draw the base line

7. What is the angle between the two arms of an equilateral triangle?
A. 30°
B. 60°
C. 90°
D. 120°
Answer: B. 60°

8. What tool is essential for verifying the accuracy of an angle drawn with a compass?
A. Divider
B. Set square
C. Ruler
D. Protractor
Answer: D. Protractor

Problem 1: Perpendicular Line Through a Point on a Segment

Question: Construct a line segment AB of length 10 cm. Mark a point P on AB such that AP = 4 cm. Draw a perpendicular line through P to AB.
Solution:

1. Begin by drawing a straight line L on your paper.
2. Place your compass needle at a point on L and label it A.
3. Set your compass width to 10 cm and mark point B on line L.
4. Measure 4 cm from point A along AB and mark this position as point P.
5. With P as center and any convenient radius, draw an arc that intersects line AB at two points (C and D).
6. Without changing the compass width, place the compass needle at C and draw an arc above line AB.
7. Now place the compass needle at D and draw another arc that intersects the previous arc at point Q.
8. Draw a line connecting P and Q, extending it in both directions.
9. This line PQ is perpendicular to AB, passing through point P.

Problem 2: Perpendicular from a Point to an Angle Arm

Question: Using a protractor, construct angle BAC measuring 70°. On side AC, mark a point P such that AP = 2 cm. From P, draw a line perpendicular to AB.
Solution:

1. Draw a horizontal line and mark a point A on it.
2. Place the protractor's center point at A, aligning its base with the horizontal line.
3. Mark a point at the 70° reading and label it B. Draw line segment AB.
4. Extend the horizontal line from A in the opposite direction of B to create line AC.
5. Measure 2 cm from A along AC and mark this point as P.
6. With P as center and a suitable radius, draw an arc that intersects line AB at point D.
7. With the same radius, place the compass at D and draw an arc above line AB.
8. Keeping the same radius, place the compass at P and draw another arc that intersects the previous arc at point E.
9. Draw line PE, which is perpendicular to line AB.

Problem 3: Parallel Perpendicular Lines

Question: Construct a line segment AB of length 8 cm. At each end of this segment, draw a line perpendicular to AB. Are these two lines parallel?
Solution:

Draw a line segment AB measuring exactly 8 cm using a ruler.

To construct a perpendicular at point A:

1. With A as center and a convenient radius, draw an arc that intersects AB at point C.
2. Without changing the compass width, place the compass at C and draw an arc above line AB.
3. With the same radius, place the compass at A and draw another arc that intersects the previous arc at point D.
4. Draw line AD and extend it in both directions to create line L₁.

To construct a perpendicular at point B:

1. With B as center and a convenient radius, draw an arc that intersects AB at point E.
2. Without changing the compass width, place the compass at E and draw an arc above line AB.
3. With the same radius, place the compass at B and draw another arc that intersects the previous arc at point F.
4. Draw line BF and extend it in both directions to create line L₂.

Analysis: Since both lines L₁ and L₂ are perpendicular to AB, they must be parallel to each other according to geometric principles.

Why Geometric Construction Matters – Key Benefits & Uses

1.  Builds Strong Foundation in Geometry
   Helps students understand basic geometric concepts by drawing shapes like angles, triangles, circles, and line segments accurately.
2. Improves Precision and Accuracy
   Using tools like a ruler and compass, students learn how to measure and construct with exactness—an essential math skill.
3. Boosts Logical Thinking and Visualization
   Constructing geometric figures enhances visual learning and problem-solving abilities.
4. Supports Real-Life Applications
   Geometry is used in architecture, design, construction, and engineering—knowing how to construct figures is a real-world skill.
5. Useful for Exams and Higher Studies
   Mastering constructions now helps in advanced geometry topics in higher classes and competitive exams.
6. Fun and Engaging for Students
   Drawing with a purpose makes math hands-on, creative, and enjoyable for many learners.
7. Encourages Neatness and Measurement Skills
   Students also learn the importance of clean, clear work using a sharp pencil and accurate tools.