# NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Written by Team Trustudies
Updated at 2021-05-07

## NCERT solutions for class 6 Maths Chapter 14 Practical Geometry Exercise 14.1

Q.1 Draw a circle of radius 3.2 cm.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

(a) Open the compass for the required radius of 3.2 cm.
(b) Make a point with a sharp pencil where we want the centre of circle to be.
(c) Name it O.
(d) Place the pointer of compasses on O.
(e) Turn the compasses slowly to draw the circle.

Q.2 With the same centre O, draw two circles of radii 4 cm and 2.5 cm.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Take centre O and open the compass up to 4 cm.

Draw a circle keeping the needle fixed at O.

Take the same centre O and open the compass up to 2.5 cm, and draw another circle.

The figure shows the required two circles with the same centre.

Q.3 Draw a circle and any two of its diameters. If you join the ends of these diameters, what is the figure obtained? What figure is obtained if the diameters are perpendicular to each other? How do you check your answer?

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

(i) By joining the ends of two diameters, we get a rectangle. By measuring, we find AB = CD and BC = AD i.e., pairs
of opposite sides are equal and also $$\angle$$ A = $$\angle$$ B = $$\angle$$ C = $$\angle$$ D = 90 , 
, i.e. each angle is of 90 .
Henc,e it is a rectangle.
(ii) If the diameters are perpendicular to each other, then by joining the ends of two diameters, we get a square.
By measuring, we find that AB = BC = CD = DA = i.e.,
all four sides are equal.
Also ? A = ? B = ? C = ? D = 90 , 
, i.e. each angle is of 90 .
Hence, it is a square.

Q.4 Draw any circle and mark points A, B and C such that
(a) A is on the circle.
(b) B is in the interior of the circle.
(c) C is in the exterior of the circle.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.5 Let A, B be the centres of the two circles of equal radii. Draw them so that each one of them passes through the centre of the other. Let them intersect at C and D.
Examine whether$$\overline{AB}$$ and $$\overline{CD}$$ are at right angles.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

## NCERT solutions for class 6 Maths Chapter 14 Practical Geometry Exercise 14.2

Q.1 Draw a line segment of length 7.3 cm using a ruler.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.2 Construct a line segment of length 5.6 cm using ruler and compasses.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

(i) Draw a line 'l 'Mark a point A on this line.
(ii) Place the compasses pointer on zero mark of the ruler. Open it to place the pencil pointup to 5.6 cm mark.
(iii) Without changing the opening of the compasses. Place the pointer on A and cut an arc' l ' at B. AB is the required line segment of length 5.6 cm.

Q.3 Construct $$\overline{AB}$$ of length 7.8 cm. From this, cut off $$\overline{AC}$$ of length 4.7 cm. Measure $$\overline{BC} .$$

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

(i) Place the zero mark of the ruler at A.
(ii) Mark a point B at a distance 7.8 cm from A.
(iii) Again, mark a point C at a distance 4.7 from A.
(iv) By measuring BC , we find that BC = 3.1 cm

Q.4 Given $$\overline{AB}$$ of length 3.9 cm. Construct (\overline{PQ} \) such that the length of (\overline{PQ} \) is twice that of (\overline{AB} \) . Verify by measurement.

(Hint : Construct $$\overline{PX}$$ such that the length of $$\overline{PX}$$ = length of $$\overline{AB}$$ then cut off $$\overline{XQ}$$ such that $$\overline{XQ}$$ also has the length of $$\overline{AB}$$ .

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.5 Given $$\overline{AB}$$ of length 7.3 cm and $$\overline{CD}$$ of length 3.4 cm, construct a line segment $$\overline{XY}$$ such that the length of XY is equal to the difference between the length of $$\overline{AB}$$ and $$\overline{CD}$$ . Verify the measurement.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

(i) Construct $$\overline{AB}$$ = 7.3 cm and $$\overline{CD}$$ = 3.4 cm.
(ii) Take a point P on the given line l.
(iii) Construct $$\overline{PR}$$ such that $$\overline{PR}$$ = $$\overline{AB}$$ = 7.3 cm.
(IV) Construct $$\overline{RQ}$$ = $$\overline{CD}$$ = 3.4 cm such that PQ = $$\overline{AB}$$ – $$\overline{CD}$$ .
Verification : On measuring, we observe that $$\overline{PQ}$$ = 3.9 cm = 7.3 cm - 3.4 cm. = $$\overline{AB}$$ – $$\overline{CD}$$
Thus, $$\overline{PQ}$$ = $$\overline{AB}$$ – $$\overline{CD}$$.

## NCERT solutions for class 6 Maths Chapter 14 Practical Geometry Exercise 14.3

Q.1 Draw any line segment $$\overline{PQ}$$ . Without measuring $$\overline{PQ}$$ , construct a copy of $$\overline{PQ}$$ .

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

I : Draw $$\overline{PQ}$$ of unknown length.
II : Draw a line l and mark a point A on it.
III: Open the compass equal to PQ.
IV : Place the needle of the compass at A and mark a point B on l.
Thus, $$\overline{AB}$$ is a copy of $$\overline{PQ}$$.

Q.2 Given some line segment $$\overline{AB}$$ whose length you do not know, construct $$\overline{PQ}$$ such that the length of $$\overline{PQ}$$ is twice that of $$\overline{AB}$$ .

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

I : Draw $$\overline{AB}$$of any suitable length.
II : Place the needle of the compass at A and the other pencil end at B.
III : Draw a line l and take a point P on it.
IV: With the same opening of the compass, place the needle at P and mark another point Q on l.
Thus $$\overline{PQ}$$ is the required line segment
whose length is twice the length of $$\overline{AB}$$ i.e $$\overline{PQ}$$ = 2$$\overline{AB}$$ .

## NCERT solutions for class 6 Maths Chapter 14 Practical Geometry Exercise 14.4

Q.1 Draw any line segment $$\overline{AB}$$ . Make any point M on it. Through M, draw a perpendicular to $$\overline{AB}$$. (Use ruler and Compasses)

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.2 Draw any line segment $$\overline{PQ}$$ . Take any point R not on it. Through R, draw a perpendicular to $$\overline{PQ}$$ . (Use ruler and set square).

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

(i) Place a set-square on PQ such that one arm of its right angle aligns along PQ
(ii) Place a ruler along the edge opposite to the right angle of the set-square.
(iii) Hold the ruler fixed. Slide the set square along the ruler till the point R touches the other arm of the set square.
(iv) Join RM along the edge through R meeting PQ at M. Then RM perpendicular PQ.

Q.3 Draw any line segment $$\overline{PQ}$$ . Take any point R not on it. Through R, draw a perpendicular to $$\overline{PQ}$$. (Use ruler and set square).

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

## NCERT solutions for class 6 Maths Chapter 14 Practical Geometry Exercise 14.5

Q.1 Draw AB of length 7.3 cm and find its axis of symmetry.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.2 Draw a line segment of length 9.5 cm and construct its perpendicular bisector.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.3 Draw the perpendicular bisector of $$\overline{XY}$$ whose length is 10.3 cm. (a) Take any point P on the bisector drawn. Examine whether PX = PY. (b) If M is the midpoint of $$\overline{XY}$$ . What can you say about the length of MX and MY?

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

On measuring, $$\overline{MX}$$= $$\overline{MY}$$ = 12 XY = 5.15 cm.

Q.4 Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.5 With $$\overline{PQ}$$of length 6.1 cm as diameter, draw a circle.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.6 Draw a circle with centre C and radius 3.4 cm. Draw any chord $$\overline{AB}$$ . Construct the perpendicular bisector of $$\overline{AB}$$ and examine if it passes through C.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.7 Repeat Question number 6, if $$\overline{AB}$$ happens to be a diameter.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.8 Draw a circle of radius 4 cm. Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.9 Draw any angle with vertex O. Take a point A on one of its arms and B on another such that OA = OB. Draw the perpendicular bisectors of $$\overline{OA}$$ and $$\overline{OB}$$ . Let them meet at P. Is PA = PB?

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

## NCERT solutions for class 6 Maths Chapter 14 Practical Geometry Exercise 14.6

Q.1 Draw $$\angle$$POQ of measure 75° and find its line of symmetry.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

$$\angle$$POA = 75°

Q.2 Draw an angle of measure 147° and construct its bisector.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.3 Draw a right angle and construct its bisector.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

$$\angle$$ COQ = 45°

Q.4 Draw an angle of measure 153° and divide it into four equal parts.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.5 Construct with ruler and compasses, angles of following measures:
(a) 60°
(b) 30°
(c) 90°
(d) 120°
(e) 45°
(f) 135°

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.6 Draw an angle of measure 45° and bisect it.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.7 Draw an angle of measure 135° and bisect it.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

$$\angle$$EOQ = $$67\frac{1}{2}$$

Q.8 Draw an angle of 70°. Make a copy of it using only a straight edge and compasses.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

$$\angle$$POQ = $$\angle$$XAY = 70°

Q.9 Draw an angle of 40°. Copy its supplementary angle.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry