NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Q.1 Draw a circle of radius 3.2 cm.

Answer :

(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.

Answer :

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?

Answer :

(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 $\mathrm{?}$ A = $\mathrm{?}$ B = $\mathrm{?}$ C = $\mathrm{?}$ 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.

Answer :

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.

Answer :

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

Answer :

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

Answer :

(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 $\overline{BC}.$

Answer :

(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 $\overline{AB}$ .

Answer :

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.

Answer :

(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, $\overline{PQ}$ = $\overline{AB}$ – $\overline{CD}$.

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

Answer :

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 $\overline{AB}$ .

Answer :

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$\overline{AB}$ .

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)

Answer :

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).

Answer :

(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).

Answer :

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

Answer :

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

Answer :

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?

Answer :

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.

Answer :

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

Answer :

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.

Answer :

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

Answer :

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?

Answer :

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?

Answer :

Q.1 Draw $\mathrm{?}$POQ of measure 75° and find its line of symmetry.

Answer :

$\mathrm{?}$POA = 75°

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

Answer :

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

Answer :

$\mathrm{?}$ COQ = 45°

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

Answer :

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

Answer :

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

Answer :

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

Answer :

$\mathrm{?}$EOQ = $67\frac{1}{2}$

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

Answer :

$\mathrm{?}$POQ = $\mathrm{?}$XAY = 70°

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

Answer :