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**NCERT solutions for Maths Practical geometry Download as PDF**

## NCERT Solutions for Class 6 Maths Practical geometry

**Class –VI Mathematics **

**(Ex. 14.5)**

**Question 1.**Draw {tex}\overline {{\text{AB}}} {/tex} of length 7.3 cm and find its axis of symmetry.

**Answer:** Axis of symmetry of line segment {tex}\overline {{\text{AB}}} {/tex} will be the perpendicular bisector of {tex}\overline {{\text{AB}}} .{/tex} So, draw the perpendicular bisector of AB.

**Steps of construction**:

(i) Draw a line segment {tex}\overline {{\text{AB}}} {/tex} = 7.3 cm

(ii) Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C and D.

(iii) Join CD. Then CD is the axis of symmetry of the line segment AB.

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

**Answer: Steps of construction**:

(i) Draw a line segment {tex}\overline {{\text{AB}}} {/tex} = 9.5 cm

(ii) Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C and D.

(iii) Join CD. Then CD is the perpendicular bisector of {tex}\overline {{\text{AB}}} {/tex}.

NCERT Solutions for Class 6 Maths Exercise 14.5

**Question 3.**Draw the perpendicular bisector of {tex}\overline {{\text{XY}}} {/tex} whose length is 10.3 cm.

(a) Take any point P on the bisector drawn. Examine whether PX = PY.

(b) If M is the mid-point of {tex}\overline {{\text{XY}}} {/tex}, what can you say about the lengths MX and XY?

**Answer: Steps of construction**:

(i) Draw a line segment {tex}\overline {{\text{XY}}} {/tex} = 10.3 cm

(ii) Taking X and Y as centres and radius more than half of AB, draw two arcs which intersect each other at C and D.

(iii) Join CD. Then CD is the required perpendicular bisector of {tex}\overline {{\text{XY}}} {/tex}.

Now:

(a) Take any point P on the bisector drawn. With the help of divider we can check that {tex}\overline {{\text{PX}}} = \overline {{\text{PY}}} {/tex}.

(b) If M is the mid-point of {tex}\overline {{\text{XY}}} ,{/tex} then {tex}\overline {{\text{MX}}} = \frac{1}{2}\overline {{\text{XY}}} {/tex}.

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

**Answer: Steps of construction**:

(i) Draw a line segment AB = 12.8 cm

(ii) Draw the perpendicular bisector of {tex}\overline {{\text{AB}}} {/tex} which cuts it at C. Thus, C is the mid-point of {tex}\overline {{\text{AB}}} .{/tex}

(iii) Draw the perpendicular bisector of {tex}\overline {{\text{AC}}} {/tex} which cuts it at D. Thus D is the mid-point of .

(iv) Again, draw the perpendicular bisector of {tex}\overline {{\text{CB}}} {/tex} which cuts it at E. Thus, E is the mid-point of {tex}\overline {{\text{CB}}} {/tex}.

(v) Now, point C, D and E divide the line segment {tex}\overline {{\text{AB}}} {/tex} in the four equal parts.

(vi) By actual measurement, we find that

{tex}\overline {{\text{AD}}} = \overline {{\text{DC}}} = \overline {{\text{CE}}} = \overline {{\text{EB}}} = 3.2{/tex} cm

NCERT Solutions for Class 6 Maths Exercise 14.5

**Question 5.**With {tex}\overline {{\text{PQ}}} {/tex} of length 6.1 cm as diameter, draw a circle.

**Answer: Steps of construction**:

(i) Draw a line segment {tex}\overline {{\text{PQ}}} {/tex} = 6.1 cm.

(ii) Draw the perpendicular bisector of PQ which cuts, it at O. Thus O is the mid-point of {tex}\overline {{\text{PQ}}} {/tex}.

Taking O as centre and OP or OQ as radius draw a circle where diameter is the line segment {tex}\overline {{\text{PQ}}} {/tex}.

**Question 6.**Draw a circle with centre C and radius 3.4 cm. Draw any chord {tex}\overline {{\text{AB}}} .{/tex} Construct the perpendicular bisector {tex}\overline {{\text{AB}}} {/tex} and examine if it passes through C.

**Answer: Steps of construction**:

(i) Draw a circle with centre C and radius 3.4 cm.

(ii) Draw any chord {tex}\overline {{\text{AB}}} .{/tex}

(iii) Taking A and B as centers and radius more than half of {tex}\overline {{\text{AB}}} ,{/tex} draw two arcs which cut each other at P and Q.

(iv) Join PQ. Then PQ is the perpendicular bisector of {tex}\overline {{\text{AB}}} .{/tex}

This perpendicular bisector of {tex}\overline {{\text{AB}}} {/tex} passes through the centre C of the circle.

NCERT Solutions for Class 6 Maths Exercise 14.5

**Question 7.**Repeat Question 6, if {tex}\overline {{\text{AB}}} {/tex} happens to be a diameter.

**Answer: Steps of construction**:

(i) Draw a circle with centre C and radius 3.4 cm.

(ii) Draw its diameter {tex}\overline {{\text{AB}}} {/tex}.

(iii) Taking A and B as centers and radius more than half of it, draw two arcs which intersect each other at P and Q.

(iv) Join PQ. Then PQ is the perpendicular bisector of {tex}\overline {{\text{AB}}} {/tex}.

We observe that this perpendicular bisector of {tex}\overline {{\text{AB}}} {/tex} passes through the centre C of the circle.

NCERT Solutions for Class 6 Maths Exercise 14.5

**Question 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: Steps of construction**:

(i) Draw the circle with O and radius 4 cm.

(ii) Draw any two chords {tex}\overline {{\text{AB}}} {/tex} and {tex}\overline {{\text{CD}}} {/tex} in this circle.

(iii) Taking A and B as centers and radius more than half AB, draw two arcs which intersect each other at E and F.

(iv) Join EF. Thus EF is the perpendicular bisector of chord {tex}\overline {{\text{CD}}} {/tex}.

(v) Similarly draw GH the perpendicular bisector of chord {tex}\overline {{\text{CD}}} {/tex}.

These two perpendicular bisectors meet at O, the centre of the circle.

NCERT Solutions for Class 6 Maths Exercise 14.5

**Question 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 {tex}\overline {{\text{OA}}} {/tex} and {tex}\overline {{\text{OB}}} .{/tex} Let them meet at P. Is PA = PB?

**Answer: Steps of construction**:

(i) Draw any angle with vertex O.

(ii) Take a point A on one of its arms and B on another such that

(iii) Draw perpendicular bisector of {tex}\overline {{\text{OA}}} {/tex} and {tex}\overline {{\text{OB}}} .{/tex}

(iv) Let them meet at P. Join PA and PB.

With the help of divider, we check that {tex}\overline {{\text{PA}}} = \overline {{\text{PB}}} .{/tex}

## NCERT Solutions for Class 6 Maths Exercise 14.5

NCERT Solutions Class 6 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 6 Maths includes text book solutions from Class 6 Maths Book . NCERT Solutions for CBSE Class 6 Maths have total 14 chapters. 6 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 6 solutions PDF and Maths ncert class 6 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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I’m telling draw angle abc=81 degree and draw its line of symmetry ok

Nice

Nice Question class 6th ncert ka liya aapna bhut kuch kiya mujhe bada acha laga thanx