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Textbook Solutions: Geometrical Constructions | Mathematics Class 6 (Maharashtra Board) PDF Download

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Chapter 17: Geometrical Constructions 
 
 
PRACTICE SET 39 [PAGE 89] 
Practice Set 39 | Q 1 | Page 89 
Draw line l. Take any point P on the line. Using a set square, draw a line perpendicular 
to line l at the point P.  
 
SOLUTION 
 
Steps of constructions: 
1. Draw line l. Take point P anywhere on the line. 
2. Place the set square on the line in such a way that the vertex of its right angle is at 
point P and one arm of the right angle falls on the line l. 
3. Draw a line PQ along the other arm of the right angle of the set square. 
4. The line PQ is perpendicular to the line l at P.  
Practice Set 39 | Q 2 | Page 89 
Draw a line AB. Using a compass, draw a line perpendicular to AB at the point B. 
 
SOLUTION 
 
Steps of construction: 
1. Draw line AB. 
2. Place the compass point on point B. Draw two arcs on either side of point B to cut the 
line AB at equal distances from B. Name the points of intersection M and N respectively. 
Page 2


Chapter 17: Geometrical Constructions 
 
 
PRACTICE SET 39 [PAGE 89] 
Practice Set 39 | Q 1 | Page 89 
Draw line l. Take any point P on the line. Using a set square, draw a line perpendicular 
to line l at the point P.  
 
SOLUTION 
 
Steps of constructions: 
1. Draw line l. Take point P anywhere on the line. 
2. Place the set square on the line in such a way that the vertex of its right angle is at 
point P and one arm of the right angle falls on the line l. 
3. Draw a line PQ along the other arm of the right angle of the set square. 
4. The line PQ is perpendicular to the line l at P.  
Practice Set 39 | Q 2 | Page 89 
Draw a line AB. Using a compass, draw a line perpendicular to AB at the point B. 
 
SOLUTION 
 
Steps of construction: 
1. Draw line AB. 
2. Place the compass point on point B. Draw two arcs on either side of point B to cut the 
line AB at equal distances from B. Name the points of intersection M and N respectively. 
3. Place the compass point at M and, taking a convenient distance greater th an half the 
length of MN, draw an arc on one side of the line. 
4. Place the compass point at N and using the same distance, draw another arc to 
intersect the first one at P. 
5. Draw a line passing through points B and P. 
6. The line BP is perpendicular to line AB at B. 
Practice Set 39 | Q 3 | Page 89 
Draw line CD. Take any point M on the line. Using a protractor, draw a line 
perpendicular to line CD at the point M. 
 
SOLUTION 
 
Steps of construction: 
1. Draw line CD. Take point M anywhere on the line. 
2. In order to draw a perpendicular through M, place the center of the protractor on point 
M. 
3. Mark a point N at the 90° mark on the protractor. 
4. Draw a line passing through points M and N. 
5. The line MN is perpendicular to line CD at M. 
 
PRACTICE SET 40 [PAGE 92] 
 
Practice Set 40 | Q 1 | Page 92 
Draw line l. Take point P anywhere outside the line. Using a set square, draw a line PQ 
perpendicular to line l. 
Page 3


Chapter 17: Geometrical Constructions 
 
 
PRACTICE SET 39 [PAGE 89] 
Practice Set 39 | Q 1 | Page 89 
Draw line l. Take any point P on the line. Using a set square, draw a line perpendicular 
to line l at the point P.  
 
SOLUTION 
 
Steps of constructions: 
1. Draw line l. Take point P anywhere on the line. 
2. Place the set square on the line in such a way that the vertex of its right angle is at 
point P and one arm of the right angle falls on the line l. 
3. Draw a line PQ along the other arm of the right angle of the set square. 
4. The line PQ is perpendicular to the line l at P.  
Practice Set 39 | Q 2 | Page 89 
Draw a line AB. Using a compass, draw a line perpendicular to AB at the point B. 
 
SOLUTION 
 
Steps of construction: 
1. Draw line AB. 
2. Place the compass point on point B. Draw two arcs on either side of point B to cut the 
line AB at equal distances from B. Name the points of intersection M and N respectively. 
3. Place the compass point at M and, taking a convenient distance greater th an half the 
length of MN, draw an arc on one side of the line. 
4. Place the compass point at N and using the same distance, draw another arc to 
intersect the first one at P. 
5. Draw a line passing through points B and P. 
6. The line BP is perpendicular to line AB at B. 
Practice Set 39 | Q 3 | Page 89 
Draw line CD. Take any point M on the line. Using a protractor, draw a line 
perpendicular to line CD at the point M. 
 
SOLUTION 
 
Steps of construction: 
1. Draw line CD. Take point M anywhere on the line. 
2. In order to draw a perpendicular through M, place the center of the protractor on point 
M. 
3. Mark a point N at the 90° mark on the protractor. 
4. Draw a line passing through points M and N. 
5. The line MN is perpendicular to line CD at M. 
 
PRACTICE SET 40 [PAGE 92] 
 
Practice Set 40 | Q 1 | Page 92 
Draw line l. Take point P anywhere outside the line. Using a set square, draw a line PQ 
perpendicular to line l. 
SOLUTION 
 
 
Steps of construction: 
1. Draw line l. Take point Q anywhere outside l. 
2. Place one of the arms of the right angle of a set square along the line l. 
3. Slide the set square along the line in such a way that the other arm of its right angle 
touches point P. 
Practice Set 40 | Q 2 | Page 92 
Draw line AB. Take point M anywhere outside the line. Using a compass and ruler, draw 
a line MN perpendicular to line AB. 
 
SOLUTION 
 
Steps of construction: 
1. Draw line AB. Take any point M outside the line. 
2. Placing the compass point at point M and using any convenient distance, draw arcs 
to cut the line AB at two points P and Q. 
3. Place the compass point at P and taking a distance greater than half of PQ, draw an 
arc on the lower side of line AB. 
4. Place the compass point at Q and using the same distance, draw an arc to cut the 
previous arc at N. 
Page 4


Chapter 17: Geometrical Constructions 
 
 
PRACTICE SET 39 [PAGE 89] 
Practice Set 39 | Q 1 | Page 89 
Draw line l. Take any point P on the line. Using a set square, draw a line perpendicular 
to line l at the point P.  
 
SOLUTION 
 
Steps of constructions: 
1. Draw line l. Take point P anywhere on the line. 
2. Place the set square on the line in such a way that the vertex of its right angle is at 
point P and one arm of the right angle falls on the line l. 
3. Draw a line PQ along the other arm of the right angle of the set square. 
4. The line PQ is perpendicular to the line l at P.  
Practice Set 39 | Q 2 | Page 89 
Draw a line AB. Using a compass, draw a line perpendicular to AB at the point B. 
 
SOLUTION 
 
Steps of construction: 
1. Draw line AB. 
2. Place the compass point on point B. Draw two arcs on either side of point B to cut the 
line AB at equal distances from B. Name the points of intersection M and N respectively. 
3. Place the compass point at M and, taking a convenient distance greater th an half the 
length of MN, draw an arc on one side of the line. 
4. Place the compass point at N and using the same distance, draw another arc to 
intersect the first one at P. 
5. Draw a line passing through points B and P. 
6. The line BP is perpendicular to line AB at B. 
Practice Set 39 | Q 3 | Page 89 
Draw line CD. Take any point M on the line. Using a protractor, draw a line 
perpendicular to line CD at the point M. 
 
SOLUTION 
 
Steps of construction: 
1. Draw line CD. Take point M anywhere on the line. 
2. In order to draw a perpendicular through M, place the center of the protractor on point 
M. 
3. Mark a point N at the 90° mark on the protractor. 
4. Draw a line passing through points M and N. 
5. The line MN is perpendicular to line CD at M. 
 
PRACTICE SET 40 [PAGE 92] 
 
Practice Set 40 | Q 1 | Page 92 
Draw line l. Take point P anywhere outside the line. Using a set square, draw a line PQ 
perpendicular to line l. 
SOLUTION 
 
 
Steps of construction: 
1. Draw line l. Take point Q anywhere outside l. 
2. Place one of the arms of the right angle of a set square along the line l. 
3. Slide the set square along the line in such a way that the other arm of its right angle 
touches point P. 
Practice Set 40 | Q 2 | Page 92 
Draw line AB. Take point M anywhere outside the line. Using a compass and ruler, draw 
a line MN perpendicular to line AB. 
 
SOLUTION 
 
Steps of construction: 
1. Draw line AB. Take any point M outside the line. 
2. Placing the compass point at point M and using any convenient distance, draw arcs 
to cut the line AB at two points P and Q. 
3. Place the compass point at P and taking a distance greater than half of PQ, draw an 
arc on the lower side of line AB. 
4. Place the compass point at Q and using the same distance, draw an arc to cut the 
previous arc at N. 
5. Draw the line MN. 
6. Line MN is perpendicular to line PQ.  
Practice Set 40 | Q 3 | Page 92 
Draw a line segment AB of length 5.5 cm. Bisect it using a compass and ruler. 
 
SOLUTION 
 
Steps of constructions: 
1. Draw seg AB of 5.5 cm. 
2. Place the compass point at A and taking a distance greater than half the length of 
seg AB, draw two arcs, one below and one above seg AB. 
3. Place the compass point at B and using the same distance draw arcs to intersect the 
previous arcs at P and Q. 
4. Draw line PQ. 
Practice Set 40 | Q 4 | Page 92 
Take a point R on line XY. Draw a line perpendicular to XY at R, using a set square. 
 
SOLUTION 
 
Steps of constructions: 
Page 5


Chapter 17: Geometrical Constructions 
 
 
PRACTICE SET 39 [PAGE 89] 
Practice Set 39 | Q 1 | Page 89 
Draw line l. Take any point P on the line. Using a set square, draw a line perpendicular 
to line l at the point P.  
 
SOLUTION 
 
Steps of constructions: 
1. Draw line l. Take point P anywhere on the line. 
2. Place the set square on the line in such a way that the vertex of its right angle is at 
point P and one arm of the right angle falls on the line l. 
3. Draw a line PQ along the other arm of the right angle of the set square. 
4. The line PQ is perpendicular to the line l at P.  
Practice Set 39 | Q 2 | Page 89 
Draw a line AB. Using a compass, draw a line perpendicular to AB at the point B. 
 
SOLUTION 
 
Steps of construction: 
1. Draw line AB. 
2. Place the compass point on point B. Draw two arcs on either side of point B to cut the 
line AB at equal distances from B. Name the points of intersection M and N respectively. 
3. Place the compass point at M and, taking a convenient distance greater th an half the 
length of MN, draw an arc on one side of the line. 
4. Place the compass point at N and using the same distance, draw another arc to 
intersect the first one at P. 
5. Draw a line passing through points B and P. 
6. The line BP is perpendicular to line AB at B. 
Practice Set 39 | Q 3 | Page 89 
Draw line CD. Take any point M on the line. Using a protractor, draw a line 
perpendicular to line CD at the point M. 
 
SOLUTION 
 
Steps of construction: 
1. Draw line CD. Take point M anywhere on the line. 
2. In order to draw a perpendicular through M, place the center of the protractor on point 
M. 
3. Mark a point N at the 90° mark on the protractor. 
4. Draw a line passing through points M and N. 
5. The line MN is perpendicular to line CD at M. 
 
PRACTICE SET 40 [PAGE 92] 
 
Practice Set 40 | Q 1 | Page 92 
Draw line l. Take point P anywhere outside the line. Using a set square, draw a line PQ 
perpendicular to line l. 
SOLUTION 
 
 
Steps of construction: 
1. Draw line l. Take point Q anywhere outside l. 
2. Place one of the arms of the right angle of a set square along the line l. 
3. Slide the set square along the line in such a way that the other arm of its right angle 
touches point P. 
Practice Set 40 | Q 2 | Page 92 
Draw line AB. Take point M anywhere outside the line. Using a compass and ruler, draw 
a line MN perpendicular to line AB. 
 
SOLUTION 
 
Steps of construction: 
1. Draw line AB. Take any point M outside the line. 
2. Placing the compass point at point M and using any convenient distance, draw arcs 
to cut the line AB at two points P and Q. 
3. Place the compass point at P and taking a distance greater than half of PQ, draw an 
arc on the lower side of line AB. 
4. Place the compass point at Q and using the same distance, draw an arc to cut the 
previous arc at N. 
5. Draw the line MN. 
6. Line MN is perpendicular to line PQ.  
Practice Set 40 | Q 3 | Page 92 
Draw a line segment AB of length 5.5 cm. Bisect it using a compass and ruler. 
 
SOLUTION 
 
Steps of constructions: 
1. Draw seg AB of 5.5 cm. 
2. Place the compass point at A and taking a distance greater than half the length of 
seg AB, draw two arcs, one below and one above seg AB. 
3. Place the compass point at B and using the same distance draw arcs to intersect the 
previous arcs at P and Q. 
4. Draw line PQ. 
Practice Set 40 | Q 4 | Page 92 
Take a point R on line XY. Draw a line perpendicular to XY at R, using a set square. 
 
SOLUTION 
 
Steps of constructions: 
1. Draw line XY. Take point R anywhere on the line. 
2. Place the set square on the line in such a way that the vertex of its right angle is at 
point R and one arm of the right angle falls on line XY. 
3. Draw a line PQ along the other arm of the right angle of the set square. 
4. The line RS is perpendicular to the line XY at R.
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FAQs on Textbook Solutions: Geometrical Constructions - Mathematics Class 6 (Maharashtra Board)

1. What are the basic geometric constructions that a Class 6 student should know?
Ans. A Class 6 student should be familiar with basic geometric constructions such as drawing a straight line, creating angles (like 30°, 45°, and 60°), bisecting angles, constructing perpendicular lines, and drawing circles. Understanding these fundamental constructions lays the groundwork for more advanced geometric concepts.
2. Why are geometric constructions important in mathematics?
Ans. Geometric constructions are important in mathematics as they help students develop spatial reasoning and visualization skills. They also provide a practical application of geometric principles, enabling students to understand the relationships between different shapes and angles, which is essential for problem-solving in geometry and other areas of mathematics.
3. What tools are commonly used for geometric constructions in Class 6?
Ans. The common tools used for geometric constructions include a straightedge (ruler without markings), a compass, and a protractor. These tools help students accurately create and measure lines, angles, and circles, which are essential for performing geometric tasks.
4. How can students practice geometric constructions effectively?
Ans. Students can practice geometric constructions effectively by working through exercises in their textbooks, using geometric software, or engaging in hands-on activities with paper and drawing tools. Additionally, following step-by-step instructions and repeating constructions can enhance their skills and confidence in geometry.
5. What role does understanding geometric constructions play in higher-level mathematics?
Ans. Understanding geometric constructions plays a crucial role in higher-level mathematics as it forms the foundation for more complex concepts such as proofs, theorems, and coordinate geometry. Mastery of these basic constructions allows students to tackle advanced topics with greater ease and enhances their overall mathematical reasoning abilities.
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Oct 14, 2025 Last updated
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