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Exercise 14.5 - Chapter 14 Practical geometry class 6 ncert solutions Maths - SaraNextGen [2024]


Question 1:

Draw https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3199/Exercise%2014_html_m23a827c5.gif of length 7.3 cm and find its axis of symmetry.

Answer:

The below given steps will be followed to construct https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3199/Exercise%2014_html_m23a827c5.gif of length 7.3 cm and to find its axis of symmetry.

(1) Draw a line segmenthttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3199/Exercise%2014_html_m38909e4e.gif  of 7.3 cm.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3199/Exercise%2014_html_14e4472d.jpg

(2) Taking A as centre, draw a circle by using compasses. The radius of circle should be more than half the length ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3199/Exercise%2014_html_m38909e4e.gif .

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3199/Exercise%2014_html_m5248905c.jpg

(3) With the same radius as before, draw another circle using compasses while taking point B as centre. Let it cut the previous circle at C and D.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3199/Exercise%2014_html_m19dd4ef5.jpg

(4) Joinhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3199/Exercise%2014_html_3aec6c9c.gifhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3199/Exercise%2014_html_3aec6c9c.gif  is the axis of symmetry.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3199/Exercise%2014_html_77ec0e5e.jpg

Question 2:

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

Answer:

The below given steps will be followed to construct a line segment of length 9.5 cm and its perpendicular bisector.

(1) Draw a line segmenthttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3204/Exercise%2014_html_7e2611f6.gif  of 9.5 cm.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3204/Exercise%2014_html_24dbdd79.jpg

(2) Taking P as centre, draw a circle by using compasses. The radius of circle should be more than half the length of https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3204/Exercise%2014_html_7e2611f6.gif .

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3204/Exercise%2014_html_1918697f.jpg

(3) With the same radius as before, draw another circle using compasses while taking point Q as centre. Let it cut the previous circle at R and S.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3204/Exercise%2014_html_67adafff.jpg

(4) Join RS. https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3204/Exercise%2014_html_25495e86.gif  is the axis of symmetry i.e., the perpendicular bisector of line https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3204/Exercise%2014_html_7e2611f6.gif .

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3204/Exercise%2014_html_m4853f099.jpg

Question 3:

Draw the perpendicular bisector ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m4bd03804.gif 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 ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m4bd03804.gif , what can you say about the lengths MX and XY?

Answer:

(1) Draw a line segmenthttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m50e8818b.gif  of 10.3 cm.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m77c8188f.jpg

(2) Taking point X as centre, draw a circle by using compasses. The radius of circle should be more than half the length of https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m50e8818b.gif .

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m3e83c145.jpg

(3) With the same radius as before, draw another circle using compasses while taking point Y as centre. Let it cut the previous circle at A and B.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m8da91b4.jpg

(4) Joinhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m38909e4e.gifhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m38909e4e.gif  is the axis of symmetry.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_2724ced4.jpg

(a) Take any point P on https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m38909e4e.gif . We will find that the measures of the lengths of PX and PY are same.

It is because https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m38909e4e.gif is the axis of symmetry. Hence, any point lying on https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m38909e4e.gif will be at the same distance from both the ends ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m50e8818b.gif .

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_71efe652.jpg

(b) M is the mid-point ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m50e8818b.gif . Perpendicular bisector https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m38909e4e.gif will be passing through point M. Hence, length ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m50e8818b.gif is just double ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_m6acb452a.gif .

Or, 2MX = XY

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3208/Exercise%2014_html_78cbc445.jpg

Question 4:

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

Answer:

(1) Draw a line segmenthttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3210/Exercise%2014_html_m50e8818b.gif of 12.8 cm.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3210/Exercise%2014_html_m29895745.jpg

(2) Draw a circle, while taking point X as centre and radius more than half of XY.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3210/Exercise%2014_html_m5e2023b1.jpg

(3) With same radius and taking centre as Y, again draw arcs to cut the circle at A and B. Join AB which intersectshttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3210/Exercise%2014_html_m50e8818b.gif at M.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3210/Exercise%2014_html_70e7cd9d.jpg

(4) Taking X and Y as centres, draw two circles with radius more than half ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3210/Exercise%2014_html_mdb93f27.gif .

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3210/Exercise%2014_html_m53c7f4a.jpg

(5) With same radius and taking M as centre, draw arcs to intersect these circles at P, Q and R, S.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3210/Exercise%2014_html_3c96740e.jpg

(6) Join PQ and RS. These are intersectinghttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3210/Exercise%2014_html_m50e8818b.gif at T and U.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3210/Exercise%2014_html_3212ef7e.jpg

(7) Now, https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3210/Exercise%2014_html_m1783a1b6.gif . These are 4 equal parts ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3210/Exercise%2014_html_m50e8818b.gif .

By measuring these line segments with the help of ruler, we will find that each is of 3.2 cm.

Question 5:

With https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3215/Exercise%2014_html_651ea87f.gif of length 6.1 cm as diameter draw a circle.

Answer:

(1) Draw a line segmenthttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3215/Exercise%2014_html_7e2611f6.gif of 6.1 cm.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3215/Exercise%2014_html_m7c8d4d05.jpg

(2) Taking point P as centre and radius more than half ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3215/Exercise%2014_html_7e2611f6.gif , draw a circle.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3215/Exercise%2014_html_mfa3ad03.jpg

(3) With same radius and taking Q as centre, draw arcs to intersect this circle at points R and S.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3215/Exercise%2014_html_m2a71fa34.jpg

(4) Join RS which intersectshttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3215/Exercise%2014_html_7e2611f6.gif  at T.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3215/Exercise%2014_html_4ba2b2b5.jpg

(5) Taking T as centre and with radius TP, draw a circle which will also pass through Q. It is the required circle.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3215/Exercise%2014_html_m3a65fd28.jpg

Question 6:

Draw a circle with centre C and radius 3.4 cm. Draw any chordhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3219/Exercise%2014_html_m23a827c5.gif . Construct the perpendicular bisector of https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3219/Exercise%2014_html_m23a827c5.gif and examine if it passes through C.

Answer:

(1) Mark any point C on the sheet.

(2) By adjusting the compasses up to 3.4 cm and by putting the pointer of the compasses at point C, turn the compasses slowly to draw the circle. It is the required circle of 3.4 cm radius.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3219/Exercise%2014_html_m38d62f3e.jpg

(3) Now, mark any chordhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3219/Exercise%2014_html_m38909e4e.gif in the circle.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3219/Exercise%2014_html_499fa62e.jpg

(4) Taking A and B as centres, draw arcs on both sides ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3219/Exercise%2014_html_m38909e4e.gif . Let these intersect each other at D and E.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3219/Exercise%2014_html_4a52c772.jpg

(5) Join DE, which is the perpendicular bisector of AB.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3219/Exercise%2014_html_m2db8d093.jpg

Whenhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3219/Exercise%2014_html_1f738f88.gif is extended, it will pass through point C.

Question 7:

Repeat Question 6, if https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3224/Exercise%2014_html_m23a827c5.gif happens to be a diameter.

Answer:

(1) Mark any point C on the sheet.

(2) By adjusting the compasses up to 3.4 cm and by putting the pointer of the compasses at point C, turn the compasses slowly to draw the circle. It is the required circle of 3.4 cm radius.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3224/Exercise%2014_html_m38d62f3e.jpg

(3) Mark any diameterhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3224/Exercise%2014_html_m38909e4e.gif in the circle.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3224/Exercise%2014_html_53537cc8.jpg

(4) Now, taking A and B as centres, draw arcs on both sides ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3224/Exercise%2014_html_m38909e4e.gif  taking radius more thanhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3224/Exercise%2014_html_m38909e4e.gif . Let these intersect each other at D and E.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3224/Exercise%2014_html_72e6df45.jpg

(5) Join DE, which is the perpendicular bisector of AB.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3224/Exercise%2014_html_559522a9.jpg

It can be observed that https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3224/Exercise%2014_html_1f738f88.gif is passing through the centre C of the circle.

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:

(1) Mark any point C on the sheet. Now, by adjusting the compasses up to

4 cm and by putting the pointer of compasses at point C, turn the compasses slowly to draw the circle. It is the required circle of 4 cm radius.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3232/Exercise%2014_html_m75e58490.jpg

(2) Take any two chordshttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3232/Exercise%2014_html_m38909e4e.gif andhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3232/Exercise%2014_html_3aec6c9c.gif in the circle.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3232/Exercise%2014_html_3e4d03ed.jpg

(3) Taking A and B as centres and with radius more than half ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3232/Exercise%2014_html_m38909e4e.gif , draw arcs on both sides of AB, intersecting each other at E, F. Join EF which is the perpendicular bisector of AB.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3232/Exercise%2014_html_4a65f557.jpg

(4) Taking C and D as centres and with radius more than half ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3232/Exercise%2014_html_3aec6c9c.gif , draw arcs on both sides of CD, intersecting each other at G, H. Join GH which is the perpendicular bisector of CD.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3232/Exercise%2014_html_3148b8a2.jpg

Now, we will find that when EF and GH are extended, they meet at the centre of the circle i.e., point O.

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 https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3237/Exercise%2014_html_m13904ac9.gif andhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3237/Exercise%2014_html_m75fe5494.gif .

Let them meet at P. Is PA = PB?

Answer:

(1)Draw any angle whose vertex is O.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3237/Exercise%2014_html_m235ab9c6.jpg

(2) With a convenient radius, draw arcs on both rays of this angle while taking O as centre. Let these points be A and B.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3237/Exercise%2014_html_5c064ca5.jpg

(3) Taking O and A as centres and with radius more than half of OA, draw arcs on both sides of OA. Let these be intersecting at C and D. Join CD.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3237/Exercise%2014_html_md3ef504.jpg

(4) Similarly, we can find the perpendicular bisectorhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3237/Exercise%2014_html_326b033e.gif ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3237/Exercise%2014_html_m6ec6ed1b.gif . These perpendicular bisectorshttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3237/Exercise%2014_html_3aec6c9c.gif andhttps://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3237/Exercise%2014_html_326b033e.gif will intersect each other at P.

Now, PA and PB can be measured. These are equal in length.

https://img-nm.mnimgs.com/img/study_content/curr/1/6/1/14/3237/Exercise%2014_html_m2d81cad0.jpg

Also Read : Exercise-14.6-Chapter-14-Practical-geometry-class-6-ncert-solutions-Maths

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