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Exercise 10.1 - Chapter 10 Practical Geometry class 7 ncert solutions Maths - SaraNextGen [2024]


Question 1:

Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only.

Answer:

The steps of construction are as follows.

(i)Draw a line AB. Take a point P on it. Take a point C outside this line. Join C to P.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1439/Chapter%2010_html_10514d71.jpg

(ii)Taking P as centre and with a convenient radius, draw an arc intersecting line AB at point D and PC at point E.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1439/Chapter%2010_html_30bdd947.jpg

(iii) Taking C as centre and with the same radius as before, draw an arc FG intersecting PC at H.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1439/Chapter%2010_html_m1cea81f6.jpg

(iv) Adjust the compasses up to the length of DE. Without changing the opening of compasses and taking H as the centre, draw an arc to intersect the previously drawn arc FG at point I.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1439/Chapter%2010_html_m57fd7fd4.jpg

(v) Join the points C and I to draw a line ‘l’.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1439/Chapter%2010_html_17ceb3.jpg

This is the required line which is parallel to line AB.

Question 2:

Draw a line l. Draw a perpendicular to l at any point on l. On this perpendicular choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.

Answer:

The steps of construction are as follows.

(i) Draw a line l and take a point P on line l. Then, draw a perpendicular at point P.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1442/Chapter%2010_html_e345e5c.jpg

(ii) Adjusting the compasses up to the length of 4 cm, draw an arc to intersect this perpendicular at point X. Choose any point Y on line l. Join X to Y.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1442/Chapter%2010_html_m27543c9a.jpg

(iii) Taking Y as centre and with a convenient radius, draw an arc intersecting l at A and XY at B.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1442/Chapter%2010_html_5aecf8e0.jpg

(iv) Taking X as centre and with the same radius as before, draw an arc CD cutting XY at E.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1442/Chapter%2010_html_65ba7c2d.jpg

(v)Adjust the compasses up to the length of AB. Without changing the opening of compasses and taking E as the centre, draw an arc to intersect the previously drawn arc CD at point F.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1442/Chapter%2010_html_7d17c8d8.jpg

(vi) Join the points X and F to draw a line m.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1442/Chapter%2010_html_m40ede76.jpg

Line m is the required line which is parallel to line l.

Question 3:

Let l be a line and P be a point not on l. Through P, draw a line m parallel to l. Now join P to any point Q on l. Choose any other point R on m. Through R, draw a line parallel to PQ. Let this meet l at S. What shape do the two sets of parallel lines enclose?

Answer:

The steps of construction are as follows.

(i)Draw a line l and take a point A on it. Take a point P not on l and join A to P.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1445/Chapter%2010_html_1d121036.jpg

(ii) Taking A as centre and with a convenient radius, draw an arc cutting l at B and AP at C.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1445/Chapter%2010_html_m59995ebd.jpg

(iii)Taking P as centre and with the same radius as before, draw an arc DE to intersect AP at F.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1445/Chapter%2010_html_m2ce1edd3.jpg

(iv) Adjust the compasses up to the length of BC. Without changing the opening of compasses and taking F as the centre, draw an arc to intersect the previously drawn arc DE at point G.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1445/Chapter%2010_html_m6ef319e3.jpg

(v)Join P to G to draw a line m. Line m will be parallel to line l.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1445/Chapter%2010_html_m7eae576f.jpg

(vi)Join P to any point Q on line l. Choose another point R on line m. Similarly, a line can be drawn through point R and parallel to PQ.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1445/Chapter%2010_html_449d30d7.jpg

Let it meet line l at point S.

In quadrilateral PQSR, opposite lines are parallel to each other.

PQ || RS and PR || QS

Thus, the quadrilateral PQSR is a parallelogram.

Also Read : Exercise-10.2-Chapter-10-Practical-Geometry-class-7-ncert-solutions-Maths

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