NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Ex 10.1

NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Ex 10.1 are the part of NCERT Solutions for Class 7 Maths. Here you can find the NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Ex 10.1.

Ex 10.1 Class 7 Maths 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.

Solution:
Steps of construction:
(i) Draw a line AB and take a point C above it.
(ii) Take any point D on the line AB.
(iii) Join the given point C to the point D and mark ∠1 to ∠CDB.
(iv) Draw ∠1 = ∠2 at C and produce the line to both sides.
(v) MN is the required line.

Using the property of alternate angles, ∠1 = ∠2. Therefore, the line MN is parallel to the line AB.

Ex 10.1 Class 7 Maths 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.

Solution:

Steps of construction:
(i) Draw a line l and take any point P on it.
(ii) Draw a perpendicular at the point P to the line l and cut an arc PX = 4 cm.

(iii) Draw ∠2 = ∠1, i.e., 90° at point X of the line PX and produce the line both sides.
(iv) m is the required line parallel to l through X.
Using properties of alternate angles, ∠1 = ∠2. Therefore, line m is parallel to line l.

Ex 10.1 Class 7 Maths 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?

Solution:
Steps of Construction:
(i) Draw a line l and take any point P outside l.
(ii) Draw a line m parallel to l through P.
(iii) Join P and Q.
(iv) PQ makes ∠1 with l and ∠2 with m which are equal angles.
(v) Take any point R on m and draw ∠3 equal to ∠2 to meet l at S such that PQ || RS.
(vi) Since l || m and PQ || RS. Therefore, PQSR is a parallelogram.